course includes sets, number properties, open sentences ... · If he "completes" the topic unit, he...
323
DOCUMENT RESUME ED 052 959 SE 011 311 TITLE A Self-Pacing Program in Algebra, Volume 1. INSTITUTION Baltimore County Public Schools, Towson, Md.; Maryland State Dept. of Education, Baltimore. PUB DATE 70 NOTE 322p. EDRS PRICE DESCRIPTORS ABSTRACT EDRS Price MF-$0.65 HC-$13.16 *Algebra, Curriculum Development, *Curriculum Guides, *Individualized Instruction, Individualized Programs, *Mathematics Curriculum, Mathematics Education, Mathematics Materials, *Secondary School Mathematics, Teaching Guides This self-pacing program is the result of a cooperative curriculum development project between The Maryland Department of Education and The Baltimore County Schools. Included is a teachers guide for the use of the materials. The philosophy of this approach is that of individualization of instruction wherein the student moves at a pace commensurate with his ability and background. He studies a topic, either individually or with a small group, then he takes a test measuring mastery of the material. The test is marked "complete" or "incomplete." If he "completes" the topic unit, he proceeds to the next; if not, he does some remedial work until he "completes" the topic unit. It is suggested that written progress reports be kept for each student continuously and that grades for the course be based on number of units completed. The content of this course includes sets, number properties, open sentences, operations with variable expressions, functions, and graphing. Also included is an extensive itemized list of behavioral objectives for each topic, student assignment sheets for each topic, tests and keys for each topic unit. (Author/CT)
Transcript of course includes sets, number properties, open sentences ... · If he "completes" the topic unit, he...
DOCUMENT RESUME
ED 052 959 SE 011 311
TITLE A Self-Pacing Program in Algebra, Volume 1.INSTITUTION Baltimore County Public Schools, Towson, Md.;
Maryland State Dept. of Education, Baltimore.PUB DATE 70NOTE 322p.
EDRS PRICEDESCRIPTORS
ABSTRACT
EDRS Price MF-$0.65 HC-$13.16*Algebra, Curriculum Development, *CurriculumGuides, *Individualized Instruction, IndividualizedPrograms, *Mathematics Curriculum, MathematicsEducation, Mathematics Materials, *Secondary SchoolMathematics, Teaching Guides
This self-pacing program is the result of acooperative curriculum development project between The MarylandDepartment of Education and The Baltimore County Schools. Included isa teachers guide for the use of the materials. The philosophy of thisapproach is that of individualization of instruction wherein thestudent moves at a pace commensurate with his ability and background.He studies a topic, either individually or with a small group, thenhe takes a test measuring mastery of the material. The test is marked"complete" or "incomplete." If he "completes" the topic unit, heproceeds to the next; if not, he does some remedial work until he"completes" the topic unit. It is suggested that written progressreports be kept for each student continuously and that grades for thecourse be based on number of units completed. The content of thiscourse includes sets, number properties, open sentences, operationswith variable expressions, functions, and graphing. Also included isan extensive itemized list of behavioral objectives for each topic,student assignment sheets for each topic, tests and keys for eachtopic unit. (Author/CT)
A SELF-PACING PROGRAM IN ALGEBRA, VOLUME I
- A Tentative Guide -
A Cooperative Projectof
The Maryland State Department of Educationand
The Baltimore County Public Schools
,U.S. DEPARTMENT OF HEALTH,EDUCATION & WELFAREOFFICE OF EDUCATION
THIS DOCUMENT HAS BEEN REPRODUCED EXACTLY AS RECEIVED FROMTHE PERSON OR ORGANIZATION ORIGINATING IT. POINTS OF VIEW OR OPINIONS STATED DO NOT NECESSARILYREPRESENT OFFICIAL OFFICE OF EDU-CATION POSITION OR POLICY.
Prepared under the direction of
Thomas E. Rowan, State Supervisor of Mathematics
William L. Gray, Acting State Supervisor of Mathematics
Vincent Brant, Mathematics CoordinatorBaltimore County Public Schools
Committee Members
Hans E. Mitchell, General Chairman
Joseph M. McSheaRobert N. KreunenDorothy M. ShindleBeth Pearsall
Copyright 1970
James A. SensenbaughState Superintendent of SchoolsMaryland State Department of Education
Eva. L. HighElizabeth J. WilsonJudith MaxRonald Medvetz
"PERMISSION TO REPRODUCE THIS
COPYRIGHTED MATERIAL HAS BEEN GRANTED
By Benjamin P. Ebersole
Dir.Curr.Inst.ServicesTO ERIC AND ORGANIZATIONS MUTINGUNDER AGREEMENTS WITH THE U.S. OFFICE OF
EDUCATION. FURTHER REPRODUCTION OUTSIDE
THE ERIC SYSTEM REQUIRES PERMISSION OF
THE COPYRIGHT OWNER."
William S. SartoriusSuperintendentBaltimore County Public Schools
;Amt.
%." f N :1 I
MARYLAND STATE DEPARTMENT OF EDUCATION
600 WYNOMURST AVENUE, BALTIMORE 21210
The Self-Pacing Program in Algehra which this letter accompaniesthou result of a cooperative curriculum development project between
nine (,tat r. Department of Education and a local school system. We in theState Department of Education are most anxious to encourage and support:'such, ventures. Cooperation in curriculum development between our staffand that of a local school system, as well as cooperation between localschool systems, should have the effect of multiplying our availableresources.
One 01 the serious problems facing educators today is that ofrapidly increasing costs to the taxpayer. Shared efforts in curriculumconstruction which hope4u1.ly minimize duplication and maximize quality,may help to hold down these costs. At the same time, when these co-operative projects attain a product which encourages diversity andcreativeness rather than conformity, then resources can be made moreimme.liatelv available to various curriculum areas. It is hoped thatthe curri:naum materials contained herein will measure up to thesecoals and will serve as one more step toward full and effective pro-cress in mathematics education for Maryland.
Sin elv,
Iate Superintendent of Sch o
FOREWORD
In recent years, there has been increasing interest in thedevelopment of mathematics programs which emphasize individualizationof instruction. This interest has been generated by a desire to provideeach student with the opportunity to use the instructional materialsbest suited to his needs. Among the programs considered have beena number of efforts involving computer-assisted instruction, programedinstruction and self-pacing programs.
Each of the preceding programs, of necessity, requiresincreased expenditures in time, personnel, materials, and money.Of the programs considered, the self-pacing format offers increasedindividualization of instruction with minimum expenditures forspecialized materials and equipment.
The Office of Mathematics of the Board of Education ofBaltimore County, in cooperation with the Maryland State Departmentof Education has developed A Self-Pacing L.r2ea.,rn in Algebra. It
is hoped that this program will serve as a model for future effortswhich use self-pacing techniques and offer suggestions for theirimplementation.
Any suggestions for improvement of this program would begreatly appreciated. The evaluation sheet is enclosed for thispurpose.
Special thanks are offered to Mrs. Carolyn Bruder andMrs. Linda Tiernan for their untiring efforts in typing andreproducing this guide.
ii
3
TABLE OF CONTENTS
Forewordii
Philosophyiv
Suggestions for Implementation
Topical Outline1
Behavioral Objectives13
Student Assignment Sheets33
Diagnostic Tests, Appendix AA -1
Achievement Tests, Appendix B B -1
Answer Keys and Check Lists for Achievements Tests,Appendix C
Profile Sheet, Appendix D
Evaluation Sheets, Appendix E
iii
C-1
D-1
E-1
PHILOSOPHY
Educators agree that students learn at different rates.Although curriculum specialists and teachers have attempted todevise programs to meet individual needs in past years, muchwork remains to achieve the goal of individualized instruction.
There is a definite need for developing a system whichprovides for individualization of instruction and greaterflexibility. Lack of differentiation in the teaching processresults in boredom for students for whom the pace is too slowand frustration for those students for whom the pace is too fast.Often this leads to problems of classroom control and highfailure rates.
One approach which is attracting attention in educationalcircles is that of self-pacing programs, wherein the studentmoves at a pace commensurate with his ability and background.An example of efforts along this line is the Individually PrescribedInstruction program of the Oak leaf Schools in Pittsburgh. In
addition, an increasing number of textbook publishers have beeninfluenced by this trend.
Preliminary returns of experimentation and pilot programsindicate that emphasis upon student success results in a morepositive attitude by the student toward the subject, teacher, andschool environment.
Suggestions for Implementation
The successful implementation of any self-pacing program inmathematics depends upon the cooperation and teamwork of theadministration and the teaching staff.
The first administrative concern for the implementation ofa self-pacing program of instruction is the construction of theschool master schedule. To provide the necessary flexibility for sucha program classes should be scheduled in a parallel manner wheneverpossible. For example, if a school has eight algebra classes, theymight be scheduled during the same period of the day or in two blocksof four classes.
Secondly, these classes should be located in adjacent roomsor as near as possible to each other for greater flexibility. Ideally,an additional room should be assigned to the teaching staff duringeach period to provide extra space for small group instruction,independent study, student-teacher conferences, and testing.
Another feature of scheduling should be the provision of atleast one common planning period during the school day for allteachers in the program. This provides the team with opportunitiesto discuss common problems, evaluate materials, plan daily lessons,regroup students, and develop new materials.
Because of the varied activities occurring simultaneously inany self-pacing program, the teacher should be provided withsufficient paraprofessional help. The possibility of assigning studentteachers from nearby colleges to each department member shouldalso be considered. If this is not possible, one or two studentteachers might be assigned to the entire department. These collegestudents could then be assigned to the teachers indicating the greatestneed on a day-by-day basis. Besides providing a service to theteachers and students, this experience can be immensely valuable tothe professional growth of the student teacher. He will have theopportunity to work with and observe more than one experiencedteacher, work with small groups before encountering the traditionallarge class, and develop teaching skills necessary in an informalsituation.
A further source of paraprofessional help consists of studentvolunteers who are advanced in mathematics. Student volunteers canbe extremely useful in tutoring individuals within the classroom,correcting tests, and performing other clerical functions.
Also, every community contains a nucleus of parents who areeager to serve their community and schools. These people should notbe overlooked when searching for additional classroom help.
Part of the role of the teacher in the self-pacing program isto coordinate the activities of the paraprofessional team which mightconsist of a student teacher, a volunteer student, and a communityvolunteer.
Class size is an important factor in the effectiveness of aself-pacing program. Thus, the administration should make everyeffort to reduce class sizes to provide for greater individualizationof instruction. Initially, a teacher might be assigned about 20 to 25students. However, after regrouping has occurred several times,it is possible that one teacher could have a class of 35 students, whilea second teacher has only 10.
In the ideal self-pacing program a building might be designedto include large rooms with portable separators. Modular schedulingwith several consecutive modules of time devoted to independent studymay be a feature of the new curricula. It is hoped that the role of theparaprofessional will be minimized in the ideal situation by assigningseveral qualified teachers to each class.
It is evident that the role of the teacher will become morecomplex in the self-pacing program. Each teacher will direct theactivities of individual students in two or more groups. This meansthat more than one activity in the traditional ,sense must be prepared.The teacher may choose to spend the entire period instructing onegroup and providing meaningful activities for the other groups. Theselatter groups can be assigned to paraprofessional aides. *A. typicalsituation might find the teacher instructing a group of 12 to 15 studentsin one part of the room, a student teacher teaching a smaller groupof 5 to 7 students in another part of the room or in a different room,
vi
and a student volunteer helping individuals in a third place. A suggestedarrangement of the room is shown below.
The physical arrangement may change from day to day depending upon theactivities planned.
The teacher may wish to spend part of his time working with eachgroup or with individuals. These suggestions in no way exhaust the possi-bilities for grouping. It may be useful for special purposes to teach theentire section as a whole. No one method should be used exclusivelythroughout the year. All of the suggested techniques should be consideredand others explored.
One of the teacher's main responsibilities is to coordinate theactivities of all groups in his class. Daily co-lerences between theteacher and his team are esseat'Al if each group is to have the benefitof planned i:astruction. Instead of preparing one lesson for the entireclass, the teacher is responsible for plarining material for each groupin his room. Ideally, teachers in a self-pacing program will beprovided planning periods for coordination of the team activities inaddition to consultation with other members of the professional staff.
Continuous evaluation of student progress should be made.Regrouping within and between classes should be done as frequentlyas necessary on the basis of the evaluation. In general, no studentshould be a permanent member of any single group. Individuals shouldnot be placed in groups on the basis of intelligence alone.
The first activity of a self-pacing program should be a diagnostictest. The students can then be assigned to the various sections on thebasis of their background. Thus, all students in the program begin atdifferent points.
8
In order to provide for maximum flexthility, at least two typesof grouping should be utilized:
a) intra-class grouping, in which students are groupedwithin the same section under the same teacher.
b) inter-class grouping, in which students are re-assigned to different sections and teachers.
An important feature of intra-class grouping is the flexibility thatit provides. In intra- class grouping, students are regrouped daily onthe basis of their immediate needs. Intra-class grouping can beaccomplished in a variety of ways.
One method provides the opportunity for some students to workindependently using student assignment sheets for direction. Theremainder of the class can be grouped on the basis of their performanceon a drill given at the beginning of the period. The drill should containmaterial from the past several days? work. Students doing well on thedrill can proceed to new material while those who need additional workcan be directed to a review group. It is not necessary to record"grades" for these drills, since the drills should be diagnostic innature.
A second method of daily grouping is to divide the class intotwo or more groups, depending upon their progress within a given unit.
A third method requires the student to indicate verbally thearea in which he needs help. Students having similar difficulties canbe grouped accordingly. These possibilities are not intended to beexhaustive.
Inter class grouping is done less frequently. The basis ofthis type of grouping is the students performance on periodic evalua-tions by the professional staff. This evaluation is based on thejudgement of the teacher and achievement on unit tests.
The exact technique of regrouping may take several forms.If only a few students in a given class complete the unit successfully,they can move on to the next higher section. Conversely, if only a,few do not complete the unit successfully, they may either bere-assigned to a slower group within the class or to a slower sectionconducted by a different teacher.
9
The purpose of the achievement test is not to determine astudent's grade on the unit. The function of this test is to determinewhether the students' backg-ound is sufficient to insure success insubsequent units. The level of acceptable performance will varyfrom unit to unit depending upon the difficulty of the material and itsrelevance to future concepts. Acceptable scores should be determinedfor each test by the teaching staff before it is administered. Experiencemay revise the acceptance levels either upward or downward. Astudent receives either a "complete" or "incomplete" for the unit andnever a numerical or letter grade.
If the student receives a grade of "complete", he moves on tothe next unit. If a student's score is "incomplete", the teacher mustdiagnose the areas of difficulty and prescribe appropriate remedialaction. The student may be instructed to restudy the entire unit ormerely one or more topics in the unit. When he shows evidence ofhaving completed this prescribed remedial program, he is retested.This retesting may take several forms. The student may take aretest on the entire unit. Therefore, several alternate forms ofeach unit test should be available. However, a student need not retakethe entire test. The students may be tested only on those areas inwhich a lack of competence was indicated. This test may be writtenor oral. If the material still is not mastered adequately, the studentis again recycled in the remedial process. A student is permitted toprogress only when he has earned the grade of "complete". Since itvery often happens that a student must restudy a unit several times,a variety of materials other than the text should be available. Theseshould include additional texts, programmed materials, filmstrips,listening posts and recorders, overhead projectors, and remedialmaterials such as the SRA ALGEBRA KIT and MAST TEACHING.
The mobility of the students in a self-pacing program necessi-tates a different device for recording student progress than the traditionalgrade book. A more useful device is a student profile k3 he et where anentire page is devoted to each student. (See Appendix D.) When studenttransfers are made, the teachers exchange student profile sheets.The most valuable characteristic of these sheets is that they containa complete record of the student's academic progress, attendanceinformation, term grades, anecdotal records. They provide a morerealistic basis for future placement than the traditional grade.
4 sensible method of grading in a self-pacing program is toassign the higher grades to those students who have completed thegreatest number of units, while lower grades would be assigned tostudents completing lesser numbers of units at the end of the term.
10
The above ideas for implementation of a self-pacing programare merely suggestive and are not intended to be mandatory orexhaustive. Continuous evaluation and refinement of this programcan be best accomplished by the participating teachers. Your reactionsand comments will prove invaluable for subsequent revision of thiseffort.
11
TOPICAL OUTLINE
FOR
A SELF-PACING PROGRAM IN ALGEBRA
VOLUME I
UN
IT I
SET
S, S
EN
TE
NC
ES
AN
D T
HE
NU
MB
ER
LIN
ET
OPI
CA
L O
UT
LIN
E
I.Se
t mem
bers
hip,
one
- o-
one
corr
espo
nden
ce, e
mpt
y se
t.
.Su
bset
ofa
set
.
.Fi
nite
and
infi
nite
set
s.
.Sy
mbo
ls o
f eq
ualit
y an
d in
equa
lity.
.Id
entif
icat
ion
of s
ente
nces
as
equa
tions
or
ineq
ualit
ies.
The
num
ber.
line
.
.O
rder
of
oper
atio
ns a
nd s
ymbo
ls o
f gr
oupi
ng.
2
UN
IT I
IV
AR
IAB
LE
S
Var
iabl
es a
nd e
valu
atio
n of
ope
n ph
rase
s.
Fact
ors,
coe
ffic
ient
s an
d ex
pone
nts.
rans
latio
n of
Eng
lish
phra
ses
and
sent
ence
s in
to a
lgeb
raic
phr
ases
and
sen
tenc
es.
TO
PIC
AL
OU
TL
INE
3
Mg.
M.M
1.1
UN
IT I
II.
NO
N-N
EG
AT
IVE
NU
MB
ER
S O
F A
RIT
HM
ET
ICT
OPI
CA
L O
UT
LIN
E
Axi
oms
ofeq
ualit
y.
Clo
sure
pro
pert
ies
of a
dditi
onm
ultip
licat
ion.
znm
utat
ive
and
asso
ciat
ive
prop
ertie
s of
add
ition
and
mul
tiplic
atio
n.
Dis
trib
utiv
e pr
oper
ty o
f m
ultip
licat
ion
over
add
ition
.
L. d
atio
n an
d m
ultip
licat
ion
prop
ertie
s of
zer
o.
MU
ltipl
icat
ion
prop
erty
of
one.
.G
raph
s of
dir
ecte
d nu
mbe
rs.
.O
rder
of
ratio
nal n
umbe
rs.
Add
itive
inve
rse
of a
num
ber.
.A
bsol
ute
valu
e of
a n
umbe
r. -
Add
ition
, sub
trac
tion,
mul
tiplic
atio
n, a
nd d
ivis
ion
of d
irec
ted
num
bers
.
Prod
uct o
f m
onom
ials
.
ombi
natio
n of
, sim
ilar
term
s.
'7)
NE
GA
TIV
E N
UM
BE
RS
TO
PIC
AL
OU
TL
INE
5
UN
IT V
OPE
N S
EN
TE
NC
ES,
EQ
UA
TIO
NS
AN
D I
NE
QU
AL
ITIE
ST
OPI
CA
L O
UT
LIN
E
1.So
lutio
n of
ope
n se
nten
ces
by r
epla
cem
ent.
.So
lutio
n of
ope
n se
nten
ces
by th
e ad
ditio
n, s
ubtr
actio
n, m
ultip
licat
ion
and
divi
sion
pro
pert
ies
of e
qual
ity.
Solu
tion
of e
quat
ions
invo
lvin
g co
mbi
natio
n of
sim
ilar
term
s.
Solu
tion
of e
quat
ions
invo
lvin
g va
riab
les
in b
oth
mem
bers
of
the
equa
tion.
Solu
tion
of e
quat
ions
invo
lvin
g fo
rmul
as.
b.So
lutio
n of
sim
ple
ineq
ualit
ies.
6
UN
IT V
I,PO
LY
NO
MIA
LS
TO
PIC
AL
OU
TL
INE
.E
xpon
ent,
pow
er, b
ase,
coe
ffic
ient
.
Law
s of
non
-neg
ativ
e in
tegr
al e
xpon
ents
.
Add
ition
and
sub
trac
tion
of p
olyn
omia
ls.
.M
ultip
licat
ion
of p
olyn
omia
ls a
nd s
quar
es o
f bi
nom
ials
.
'vis
ion
of p
olyn
omia
ls.
SPE
CIA
L P
RO
DU
CT
S A
ND
FA
CT
OR
ING
TO
PIC
AL
OU
TL
INE
I.Fa
ctor
izat
ion
of a
n in
tege
r in
to p
rim
e in
tege
rs.
Z.
Fact
oriz
atio
n by
rem
ovin
g a
com
mon
fac
tor.
3.Pr
oduc
t of
the
sum
and
dif
fere
nce
of tw
o nu
mbe
rs.
Fact
oriz
atio
n of
the
diff
eren
ce o
f tw
o sq
uare
s.
Squa
re o
f a
bino
mia
l and
pro
duct
of
two
bino
mia
ls.
Fact
oriz
atio
n of
qua
drat
ic tr
inom
ials
.
.C
ombi
natio
ns o
f se
vera
l typ
es o
f fa
ctor
ing.
Solu
tion
of q
uadr
atic
equ
atio
ns b
y fa
ctor
ing.
UN
IT. V
III
FRA
CT
ION
ST
OPI
CA
L O
UT
LIN
E
.R
estr
ictio
ns o
n th
e va
riab
le.
Red
ucin
g fr
actio
ns.
Rat
io.
Mul
tiplic
atio
n an
d di
visi
on o
f fr
actio
ns.
Add
ition
and
sub
trac
tion
of f
ract
ions
.
Sim
plif
icat
ion
of c
ompl
ex f
ract
ions
.
Solu
tion
of o
pen
sent
ence
s w
ith f
ract
iona
l coe
ffic
ient
s.
.So
lutio
n of
fra
ctio
nal e
quat
ions
.
9
UN
IT I
XG
RA
PHS
OF
EQ
UA
TIO
NS
TO
PIC
AL
OU
TL
INE
Ope
n se
nten
ces
in tw
o va
riab
les.
Gra
phs
of p
oint
s in
the
Car
tesi
an p
lane
.
Gra
phs
of li
near
equ
atio
ns.
" .."
:'
...a.
Cha
rtM
etho
d,
thst
one
y-in
terc
ept m
etho
d
Det
erm
inat
ion
of th
e eq
uatio
n of
a li
ne g
iven
:
a.po
int a
nd s
lope
`,"
b.sl
ope
and
y-in
terc
ept
.tw
o po
ints
.
Gra
phs
of in
equa
litie
s in
two
vari
able
s.
Solu
tion
of s
imul
tane
ous
equa
tions
in tw
o va
riab
les.
grap
hic
met
hod
b.ad
ditio
n-su
btra
ctio
n m
etho
d
C.
subs
titut
ion
met
hod
d.C
ram
eigs
rul
e
- 10
-
UN
IT X
TH
E R
EA
L N
UM
BE
RS
TO
PIC
AL
OU
TL
INE
1.R
atio
nal n
umbe
rs -
fra
ctio
nal f
orm
, dec
imal
for
m.
2.Ir
ratio
nal n
umbe
rs -
roo
ts o
f ra
tiona
l num
bers
.
3.Pr
oper
ties
of ir
ratio
nal n
umbe
rs.
4.Pr
oduc
t and
quo
tient
pro
pert
ies
of r
adic
als.
5.A
dditi
on, s
ubtr
actio
n, a
nd m
ultip
licat
ion
of r
adic
als
and
quad
ratic
surd
s.
6.R
atio
naliz
atio
n of
den
omin
ator
s co
ntai
ning
rad
ical
s an
d qu
adra
tic s
urds
.
7.So
lutio
n of
ope
n se
nten
ces
cont
aini
ng r
adic
als.
UN
IT X
IR
EL
AT
ION
S, F
UN
CT
ION
S, A
ND
VA
RIA
TIO
NT
OPI
CA
L .O
UT
LIN
E
I.R
elat
ions
.
2.Fu
nctio
ns.
.Pr
opor
tion.
.D
irec
t var
iatio
n.
5.In
vers
e va
riat
ion.
- 12
-
1.
BEHAVIORAL OBJECTIVES
FOR
A SELF-PACING PROGRAM IN ALGEBRA
VOLUME I
Sets, Sentences, and the Number Line
The student should be able to:1. identify members of a set.2. list the members of a set described by a rule.3. write a rule describing a set whose members are given.4. state whether or not a one-to-one correspondence exists
betwe.en two sets.identify finite sets, infinite sets, the null set.
6. identify subsets of a given set.7. list all the subsets of a given set of three or fewer members.
state that the null set is a subset of every set and every set isa subset of itself.identify the symbols which represent the null set amongthe following list:
0
{0}
{0}
C.
10. graph appropriate sets on a number line. /These include:a. {1, 3, 5}b. {all, numbers between 3 and 5}c. {all numbers between 0 and 1 including 0 and 1d.. {all numbers greater, than 4}
11. on the number, line locate a point associated with a givencoordinate.
12. name the coordinate .5...sz-,,z;listeil with a given point on anumber Lae .
decide by computation whether the right and left hand sideof a number statement name the same number.place the proper inequality symbol, < or >, between twonumber statements to make a true inequality..
15. state that if one number is greater than a second, the former'sgraph is found further to the right than the latter's on anumber. line.
46: compute correctly the value of a number phrase by using the:Order of operations 'rules..
UNIT II. Variables
The student should be able to:1. identify (and he need not be required to write definitions for
the following terms):a. variable.
replacement set.c. constant.d. factor.
term.coefficient.exponent .
basepower .
distinenish between factors and terms.state the number of terms in an algebraic expression.write 3 times a as 3a, (3)(a), 3-a.
3given -- 7a phrase such as write its equivalent, .
distinguish between (2b) 2 and 2b by stating to which quantitythe exponent refers in each case.evaluate formulas by substituting numbers for variables.
8. write an algebraic expression representing a written, phrasesuch as 'live times a number, increased by threw',write an algebraic sentence representing a written sentencesuch as Ita number increased by five is twelveu.
UNIT III. Non-negative Numbers of Arithmetic and Elementary Structure
The student should be, able to:
1. identify the reflexive property of equality, given a statementsuch as 5 = 5.
2. identify the symmetric property of equality, given a statementsuch as 5= 3+ 2 implies 3+ 2= 5.
3. given a statement' such as 3 = 5 - 2 and 5 - 2 = 2 + 1 implies3 = 2. + 1, identify it as an application of the transitiveproperty of equality.
4. given the first two parts of the transitive property of equality,supply the third statement.state whether or not a given set of numbers is closed withrespect to a given operation.given a number sentence illustrating one of the followingproperties, identify the property:
commutative property for addition or multiplication.associative property for addition or multiplication.distributive property for multiplication over addition.
identify distinct terms involving one variable as similaror not similar.combine similar terms by addition and subtraction.identify the multiplicative property of 1 i.e. a 1 a forall numbers a.
10. identify the additive property of zero, i. e. a + = a for allnumbers a..
11. name 1 as the multiplicative identity element.12. name 0 as the additive identity element.13. identify the multiplicative property, of zero, i.e a.)(0) = 0
for all numbers
14. state that names no unique number of arithmeticconsequently one carnet divide by zero.
1S. given a series of equalities of no more than four membersand a list of the names of basic properties of equality andthe non-negative numbers of arithmetic, be able to writethe reason supporting each step.Example: Prove 3(a + b) + c = 3a + (c + 3b)
Statement Reason1. 3(a + b) + c = (3a + 3b) + c 1.
2. (3a + 3b) + c = 3a + (3b + c) 2.
3. 3a + (3b + c) = 3a + (c + 3b) 3.
4. Thus, 3(a + b) + c = 3a + (c + 3b) 4.
17. given a non-negative number of arithmetic, write itsreciprocal.
18. state the property of multiplicative inverses, i.e. a and bare multiplicative inverses if and only if (a)(b) = 1.
19. given a non-negative number of arithmetic, write itsmultiplicative inverse.state that 0 has no multiplicative inverse.
UNIT IV. Negative Numbers of Arithmetic
The student should be able to:1. construct a number line showing the integers.2. using the number line tell which of two rational numbers is
greater in value.3. arrange a set of not more than five directed numbers in
ascending or descending orderstranslate verbal statements such as "a loss of three dollarsitinto an algebraic phrase using directed numbers.
5. name the additive inverse of any given directed number.write the absolute value of any directed number.add, subtract, multiply, and divide directed numbers.state that a minus b means a plus the opposite of b.state that division is multiplication by the reciprocal ofthe divisor.state the three ways in which the minus sign is mostcommonly used in algebra, that is, as
part of the name of, some integersas the symbol which represents the operation ofsubtraction.
c. as a shorthand symbol for the phrase "the additiveinverse of"
11. add and subtract, two monomials, binomials, or trinomials,or combinations of these involving the first power of oneor two variables given in either horizontal or vertical form.
12. use the property of (-1) to write equivalent statements fora given algebraic statement. For example:
-5 = (-1)(5)-a = (-1)(a)
+, b) (-a)
UNIT V. 0 en Sentences - E uations sE lne ualities
The student should be able to:1. identify
a. open sentence.
b. equation.
c. left member.d. right member.e. solution set.1. root.g. inequality.NOTE:. Replacement sets should be given for each
problem now and throughout the course.intuitively solve simple open sentences by guessing.test by substitution whether or not a given number is theroot of a given open sentence.using pencil and paper, solve linear equations in one unknownusing the addition property of equality.using pencil and paper, solve linear equations in one unknownusing the multiplication property of equality.using pencil and paper, solve the following types of linearequations:
a. 2a - 13 = 30b. 5b + 9 - 3a = 20c. 15 - 4a.-+ 3a = 17
d. 5d = 7 = 3d,
6 (x 4) =
f. 7(y + 4) = -14g. 3(5 - z) = 7h. -6(6 - 4x) = 1
i. 5(3 + 2x) - 4x =
graph the solution sets of these above types of equations ona number line.
8. state the addition and multiplication properties of inequalities.
using pencil, paper, and the properties of, inequalities, solvethe following types of linear inequalities:a. 5a >10 e. 7(3e+ 1) - 2e > 3(2e - 1)
-6b < 13 f. a <6
d + 4 > 9 g.-3
4c < -7
d. 5(2a -1) < -4graph the solution sets of these above types of inequalitieson a number line.
UNIT VI. Polynomials,
The student should be able to:
1. identify a polynomial in one or two variables.
Z. name a polynomial according to the number of termsmonomial, binomial, and trinomial.
3. name the degree of a polynomial.4. arrange a polynomial in one variable in order of ascending
or 'descending powers of the variable.add and subtract polynomials in both horizontal and verticalnotation. (Review additive inverse of a polynomial.)state the basic laws of exponentiation in both symbols andwords:
where rn and n are positive integers.rn n mn
(a ) = a , where ni and n are positive integers.
d. + an=
where m and n are positiveintegers and zri > n.
e. in m m(ab) = a. b , where m is a positive integer.0state the definitions for a , (a A 0), and al.
where in arid n are positiveintegers and m<n.
simplify an expression involving one-step application ofthe laws 6(a) - 6(e).simplify an expression involving several applications ofthe laws 6(a) .- 6(e).
10. multiply polynomials involving the product of:a. a monomial and a polynomial of more than one term.
two polynomials of more than one term and less thanfour.
recite a rule for determining the product of two binomials(FOIL) and squaring a binomial.
12. find the product of any two binomials without penciland paper.
13. divide a polynomial of more than one term by a monomial.14. divide a polynomial of more than one term by a binomial.
UNIT vn. Seecial Products and Factoring
The student should be able to:t. distinguish between prime and composite numbers.2. write an integer as the product of prime factors.3. name the GCF of two or more integers.4. express a monomial as the product of prime factors.5. name the C(F of two or more monomials.6. name the following special products:
a.. difference of two squares.b. perfect square trinomial.
7. factor into prime factors a polynomial involving one - stepfactoring of the following types:
a. common monomial factor.b. difference of two squares.c. trinomials, general case with integral coefficients.
polynomials of four terms by grouping to reveal acommon binomial factor.
state a procedure for factoring a polynomial into primepolynomial factors.using pencil and paper, factor into prime polynomial factors,polynomials using two or more types of factoring.state that the product of two or more quantities is zero,if and only if at least one of the factors is zero.using pencil and paper, solve problems of the following types:
(x + 1) = 2 = 25
+..,1) ( 0(x - 9)
UNIT VIII. Fractions
The student should be able to;1. define a fraction as the indicated quotient of two integers
or polynomials.2. identify the numerator and denominator of a given fraction.3. determine which value or values of the variable make the
denominator of a given fraction zero and, hence, are notpermissible replacements.
4. reduce to lowest terms a fraction whose numerator anddenominator are polynomials.compute the product of two or more fractions including suchcases as:
a. 'y -x
5c23.
(2x2
x - 9x + 1 x+d. 2x + 3 x -
compute the quotient of two rational expressions.add and subtract two or more rational expressions whichhave equal denominators.calculate the LCIVi of two or more polynomials.add and subtract two or more rational expressions whichhave unequal denominators .
simplify a complex fraction whose numerator and denominatorare rational.; expressions.
. calculate the ratio of two quantities.determine the fourth term of a proportion in the form
. .solve:.equatione and inequalities with fractional coefficients.
UNIT IX. Graphs and Sentences in Two Variables
The student should be able to:1. identify:
a. coordinate axes.b. origin.c, quadrant.d. abscissa, ordinate.e. ordered pair.
2. graph an ordered pair in the Cartesian plane.3. name the quadrant in which a point lie.: given its coordinates.4. determine if a point lies on a given axis given its coordinates.
b.
7.
1 0 .
11.
12.
state that the point with coordinates (x, y) can lie in aniquadrant or on either axis.distinguish between subscripts and exponents.
solve equations of the form Ax + By + C = 0 for y in termsof x.
determine several solutions (ordered pairs) to an opensentence in two variables.graph, using the chrt method, linear equations in twovariables .
determine the x and :y intercepts of a linear equation intwo variables by (a) graphing, and (b) substitution.graph the solution set of the special cases (a) x = a and(b) y =
state the equation of the x and y axes.state, that the graph of x = a is a vertical line and that thegraph of, a is a horizontal line.
14. state whether or :not an equation is linear.lg iven the graph of a line with several given points, determine
given two points which determine a line, calculate the slopeof the'line algebraically
state that the slope of a line is constant regardless ofthe pair of points used to determine the slope.
18: state that a horizontal line has 0 slope and that thevertical line has no slope defined.
19. distinguish between positive and negative slopes and beable to state their geometric. interpretations.
20. plot a line given:a. two points.b. point- slope.
c.. slope-intercept.d. intercepts.
21. plot a line given its equation in:a. point-slope form.
b. AX By + = 0 or general form.22: write the equation of a line given:
a. its slope and y-intercept.b. its slope and the coordinates of one point on the line.c. the coordinates of two points on the line.graph inequalities of the forth:2
x'> a > x <a. and x< ay >a, Y> a, y < a, and y< aAx + By ::+ C > 0, + By + C > 0 Ax + By + C < 0,and Ax + By + C < 0
24 using the chart method graph parabolas of the form2 a- 0
2 . deterMine the common solution to a pair of linear equationsin two ,variables by each of the following methods:
raphink.
substitution--when one of the equations is "easily",solved for one of the variables. This occurs, ofcourse, when one of the variables haS a coefficient ofone.
addition-Subtractioneteri-ninants.
method .
UNIT X. The Real Numbers
The student should be able to:
1. define a rational number as the quotient of two integers.2. given an integer or a decimal with one, two or three places
of decimals, write it as a rational number.3. write a common fraction as a decimal,4. distinguish between a terminating, and periodic decimal.5. given one of the two standard notations for periodic decimals,
write the equivalent.Example: .83 = .8333...
.6363: .. = ..63NOTE: A class discussion on the principle that a rationalnumber in the forme , where p and q are relatively prime,either terminates in decimal expansion or repeats in a blockof fewer than q digits is appropriate at this time.determine by computation which of two given rational numbersis the greater in value.state the trichotomy principle for rational numbers.by averaging, determine a rational nuraber between any twogiven rational numbers.NOTE: A class discussion on the density property isappropriate at this time.given a rePeating decimal (nonterminating) of period 1 or 2,determine the equivalent rational number in the form 2
q
state the principle that all terminating decimal- and infiniteperiodic idecimals name rational numbers.state the definition of the square, cubea number.
lz. identify the index and radicand of the radical 1,Zri,
13. write the square roots of perfect squares up to 225.'14 state that square roots, of negative numbers do not exist in the
15. state the rules:
a. ( \I a )2 = a, a> 0
b. ( far-) = a, a > 0
16. use the rules developed in item 15 to simplify expressionsinvolving their one step application.
17. state the product and quotient properties of square roots:a. a = a > 0 and b > 0
NIb,
a= a> 0 and b >0
b
18. give the square roots of monomials of the form:2
100z2 c. 22_
2b. 49x2y2
NOTE: Restrictions on the variable should not beemphasized at this point. The main objective is thatthe student can apply the laws of square roots to simplifya monomial.
19. calculate square roots of such numbers as .57, .023 and.0023 by using a table of roots.distinguish between the two meanings of an expressioncontaining a radical sign, i.e. as, an operation and asnaming a number.calculate the product of two radicals using the productproperty for such problems as
NI 3 . = 21
23. simplify such radicals as:a.
c.
d.
) (
(54-b )Z
(-2 Nri. ) (6 4 ab )
j 77e. 15a2b
f. ( NifaT)-)2
g.
h.
21. 412a
j 6a7
i. ,15a?3
i 72a
13xik.2---2-
1. Ni 2Y--3x
m.Nf-ry
$Xn.'J2z
NOTE: The point is that at this level all indices shouldbe two, the quantities involved should be monomials, andonly the first and second degree should be employed.
24. identify similar terms or similar radicals in a group such as:4 3-- , ",3r3. , 7\1 .2. 24-1.
25. add and subtract radicals.26. calculate the product of binomials which contain radicals.27. determine the conjugate of real numbers of, the form:
a + b b and c
rationalize denominators of real numbers of the form:
and a NI 1; + c
+ d + g N/ h
29. solve radical equations with one radical whose radicand canbe a monomial or binomial. He must check gor extraneousroots.
30. define the real numbers as the set of all decimals.
30
UNIT XI. Relations, Functions and Variation
The student should be able to:
1. distinguish between a set of elements which are not orderedpairs and a set whose elements are ordered pairs .
2. list the first coordinates and second coordinates of a set ofordered pairs.
3. define a relation as a set of ordered pairs.4. given a finite relation in roster form, write its domain and
range.5. graph a relation, given the set of ordered pairs.S. given the graph of a relation, determine its domain and
range.given a rule (formula) graph the relation on a limited domain,i.e., a subset of the reals.given a table of values, find the graph of a relation.given a table of values, write a relation in ordered p .irnotation.
state that a relation may be defined by a set of orderedpairs, graph, formula (rule), or table of values.
11. given a table of values defining a linear relation of theform y = mx or y x + a, find the correct formula andthen determine missing values.
1 . define a function as a relation whose elements containdistinct first members.
13. given a set of ordered pairs, tell whether it defines afunction or not.write the domain and range of a function defined by
roster.table. of values.graph,
tell whether a graph defines a function or relation.6 given the set of ordered pairs, determine if it is a direct
variation.etermine by examining a linear graph, if it is one of
direct variation.
18. given a direct variation defined by a table of values, writea rule relating the domain and range, i.e., a statement of theform y = 171x.
19. given either a table of values or a rule defining a directvariation, write the constant of proportionality.
20. identify the means and extremes of a proportion given ina
dcthe form b = or a:b = c:d.
21. state the product property of proportions.22. determine whether two ratios are equal.23. solve (for a variable term in) a proportion using the product
property of proportions.24. given an English sentence describing a direct variation,
write a formula correctly describing this result.25. given a set of ordered pairs or table of values, determine
whether this describes an inverse variation.26. translate English statements concerning an inverse variation
into valid formulas.27. given a set of formulas, identify those which define a direct
variation, inverse variation, or neither.NOTE Joint variation and combined variation will notbe considered.
STUDENT ASSIGNMENT SHEETS
FOR
A SELF - PACING'' 'PROGRAM IN ALGEBRA
VOLUME I
The previous sections on Topical Sequence and BehavioralObjectives may be used with any modern algebra text. Inorder fo- teachers to see how this may be done, thefollowing section uses a typical algebra text, Modern Algebra,Book I, by Dolciani, Berman and Frei Lich as an illustration.
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x.1
-8
Do
also
:1.
5 +
(-5
) =
2.(-
7) +
(+
7) =
3.(-
3) +
(+
3) =
4.(+
7.2)
+ (
-7.2
) =
5.a
+ (
-a)
=
ASS
IGN
ME
NT
TO
PIC
RE
AD
ING
ASS
IGN
ME
NT
DA
TE
CO
MPL
ET
ED
20..
Abs
olut
e va
lue
P. 1
23P.
124
Ora
l Ex.
1-24
?add
ition
of
dire
cted
num
bers
Pp. 1
24-1
26P.
126
Ora
l Ex.
1 -1
8.P.
127
Wri
tten
Ex.
1,2,
3,5,
7-10
,13,
14,1
8,2
(-35
P. 1
28Pr
oble
ms
1, 6
22..
Subt
ract
ion
of d
irec
ted
num
bers
Pp. 1
28-1
30P.
130
Ora
l Ex.
1,4
,5,7
,9,1
1,12
,17,
18,2
0,21
,27-
32,3
6P.
131
Wri
tten
Ex.
21,
22,2
7,28
23M
ultip
licat
ion
of d
irec
ted
num
bers
Pp. 1
33-1
35P.
135
Ora
l Ex.
1-21
P. Wri
tten
Ex.
1,3,
5,11
,12,
15,1
6
ASS
IGN
ME
NT
TO
PIC
RE
AD
ING
ASS
IGN
ME
NT
DA
TE
CO
MPL
ET
ED
2.
Prod
uct o
f m
onom
ials
Det
erm
ine
the
prod
uct:
1.(3
x)(2
y)6.
(-5a
b)(-
2bc)
22.
(-4z
)(3d
)7.
( -3
x)'
I
3.(6
c)(-
411)
8.(-
5a)3
4.(-
2d)(
-4,0
9.(-
6x2)(
-3y2
)
5.(6
xy)(
-2x)
10.
(2x)
(-3y
)(-2
z)
25.
Div
isio
n of
dir
ecte
dnu
mbe
rsPp
. 138
-140
P. 1
40O
ral E
x.1-
20,3
3-42
,49,
51
26.
Com
bini
ng s
imila
r te
rms
Pp. 1
33-1
35P.
137
Wri
tten
Ex.
21-
24,2
6,27
,31-
34,3
6-44
Rem
ove
the
pare
nthe
ses
and
com
bine
sim
ilar
term
s:1.
3(x-
2)-7
Z.
-2(y
+8)
+ 3
y
3.4(
2x +
5)
+8
(-2x
-3)
4.-3
(3x
+ 7
) -i
-Z (
4x +
7)
5.-2
(-/x
+ 3
a) +
5 (i
x-
6a)
6.-1
(6x
- 3
) -5
(2x
+ 1
)7.
-4(2
a +
3b)
-7
(-3a
+ b
)8.
-5(5
y_ +
3)
--sy
+ 8
.
ISE
E I
NST
RU
CT
OR
FO
R T
EST
- 41
-
OPE
N S
EN
TE
NC
ES,
EQ
UA
TIO
NS
INE
QU
AL
ITIE
SST
UD
EN
TA
SSIG
NM
EN
T S
HE
ET
ASS
IGN
ME
NT
TO
PIC
RE
AD
ING
ASS
IGN
ME
NT
DA
TE
CO
MPL
ET
ED
27. .
29.:
Solv
ing
open
sen
tenc
es b
yre
plac
emen
t
The
add
ition
and
sub
trac
--d
on p
rope
rtie
s of
equ
ality
The
mul
tiplic
atio
n an
dch
Asi
on p
rope
rtie
s of
equa
lity
Sect
ion
2-3
Pp. 8
0-82
Pp. 8
3-84
-
I46
Ora
l Ex.
1,2,
3,4,
5,9,
15,1
7,18
,21,
22,3
0Pp
. 47-
48W
ritte
n E
x.1,
3,4
,6,7
,11,
16,1
8,19
,20
,22,
23,2
5,27
P. 8
2O
ral E
x. 1
,3,7
,11,
17,1
9P.
83
Wri
tten
Ex.
1,3
,6,7
,8,1
0,11
,21
P. 5
9Pr
oble
ms
13,1
6
Solv
e ea
ch e
quat
ion
usin
g th
e m
ulti-
plic
atio
n pr
oper
ty o
f eq
ualit
y. S
how
an in
term
edia
te s
tep.
4 d
1.5a
= 1
58.
205
2. 7
a= 2
37
9.8f
= -
213.
16 =
5b
3=
- 7
4.-
/a =
10. a
.10
64
5.--
5d =
-13
11.
--32 n
= 1
51
6.4f
= 7
53
12. -
n =
--
64
7.2 h
= -
183
- 42
-
ASS
IGN
ME
NT
TO
PIC
RE
AD
ING
ASS
IGN
ME
NT
DA
TE
CO
MPL
ET
ED
.C
ombi
ning
term
s an
d us
eof
tran
sfor
mat
ion
prin
ci-
pies
3.
Solv
ing
equa
tions
with
vari
a.ol
es in
bot
h m
embe
rsof
the
equa
tion
Pp. 8
6-88
Pp. 1
58-1
59
_
Pp. 9
1-93
d,a
13.
= 4
19.
h=
5 -5rn
-2m
14.
0=
32.
= -
5-a a
15.
1,2d
= 2
.421
.3
= 6
16.
3.9
= 1
.3f
b1
22.
=
17.
5.4
= -
1.3h
72
c3
18.
-103
= .5
a23
.=
--
-24
Pp. 8
8-89
Wri
tten
Ex.
2,3
,4,5
,7,8
,9,1
0,11
-16,
2 1,
29,3
0,36
,41,
47,4
9P.
158
Ora
l Ex.
1,2
,3,4
,5,6
,7,1
0,13
P. 5
9Pr
oble
ms
4,8
P. 9
3W
ritte
n E
x.1,
2,3,
5,6,
7,8,
9,11
,12,
14,1
5,-1
6,18
,20,
21,2
3,24
,26
,28,
30,3
1,32
P. 1
70Pr
oble
ms
1,4,
5,8
Pp. 5
8-59
Prob
lem
s1,
5, 1
5
- 43
-
1
(
ASS
IGN
ME
NT
TO
PIC
RE
AD
ING
ASS
IGN
ME
NT
32..
Solv
ing
form
ulas
Prop
ertie
s of
ineq
ualit
ies
Pp: 1
57-1
58
Pp. 1
59-1
62
P. 1
59W
ritte
n E
x. 2
,3,5
,8,1
0,11
,15,
16,2
3,24
, 25,
29,
30, 3
1, 3
3,34
, 35
P. 8
9Pr
oble
ms
1, 3
,6
P. 1
63W
ritte
n E
x.1,
2,3,
4,5
, 7,8
,11,
12,1
3,14
, 15,
20,
21,
22P.
89
Prob
lem
s 5,
10
SEE
INST
RIT
TO
RFO
R T
EST
.
- 44
-
DA
TE
CO
MPL
ET
ED
V -ASS
-4G
NM
EN
T
Subt
ract
in.g
pol
ynom
ials
The
pro
duC
t of
pow
ers
POL
YN
OM
IAL
S
RE
AD
ING
IA
SSIG
NM
EN
T
Pp. 1
97-1
98
Pp. 2
00-2
01
P. 2
03
STU
DE
NT
ASS
IGN
ME
NT
SH
EE
T
Pp: 1
98G
ra' E
x.1,
3, 4
, 5,7
, 9, 1
0, 1
1, 1
2, 1
4,7,
18,2
0,21
,22,
23,2
4,27
,29
,30,
31P.
89
- Pr
oble
ms
13, 1
7
Pp. 2
01-2
02O
ral E
x.1,
3,4,
5,6
, 9, 1
0, 1
1, 1
2,13
16, 1
7P.
202
Wri
tten
Ex.
10, 1
1, 1
2, 1
4, 1
8, Z
1P.
94
Prob
lem
s 2,
7
P. 2
04W
ritte
n E
x.3,
4, 5
, 8, 1
0, 1
2, 1
5, 1
9,20
,26
Do
the
follo
win
gpr
oble
ms:
1.23
-24
2.x
5x2
3.a1
a2a5
4.3x
6x3
30
YY
5.
DA
TE
CO
MPL
ET
ED
- 45
-
-ASS
IGN
ME
NT
TO
PIC
RE
AD
ING
ASS
IGN
ME
NT
DA
TE
CO
MPL
ET
ED
37.
The
pow
er o
f a
prod
uct
Pp; 2
04-2
05
The
Quo
tient
of
pow
ers
Pp. 2
15-2
17
3.
Zer
o as
an
expo
nent
P. 2
18
.lv
iuiti
plyi
ng p
olyn
omia
ls b
yPp
. 206
-207
a m
onom
ial
Pp. 1
78-1
80
Do
the
follo
win
g pr
oble
ms:
(ab)
26.
(-2)
2
2.(6
a)2
7.(-
L)3
3.(-
2b)2
8.(3
d2)3
4.3
(3xy
)9.
(..z
a2 )
4
5.(d
3)2
P. 2
03W
ritte
n E
x.Z
, 4,5
,6,7
,9,1
5,18
P. 2
17O
ral E
x. 1
-10
P. 2
18W
ritt
en E
x. 2
,3,4
,5,1
0,14
,15,
19,2
3
Pp. 2
18-2
19O
ral E
x. 1
-20
Pp. 2
07-2
08W
ritte
n E
x.1,
2,4,
5,6,
7,10
,12,
15,
20,2
1P.
202
Wri
tter
Ex.
17,2
0,24
,27
Pp. 2
08-2
09Pr
oble
ms
1,2,
4,9
- 46
-
ASS
IGN
ME
NT
TO
PIC
RE
AD
ING
ASS
IGN
ME
NT
DA
TE
CO
MPL
ET
ED
41..
Mul
tiplic
atio
n of
two
P. 2
09P.
210
poly
nom
ials
Wri
tten
Ex.
1,2,
3,5,
S, 7
,9, 1
0, 1
2,14
,15
,17,
19,2
0,21
,27,
28,2
933
.r
P. 2
12Pr
oble
ms
2,6
i.
Rai
sing
bin
omia
ls to
aPp
. 213
-214
P. 2
14po
wer
Wri
tten
Ex.
1,2,
3,5,
9,11
,13
P.21
4Pr
oble
ms
i
43.
Div
isio
n of
pol
ynom
ials
by
Pp. 2
19 -
220
Pp. 2
20-2
21a
mon
omia
lW
ritte
n E
x.1,
2,3,
6,7,
10,1
1,12
,13,
14,1
5,17
,18,
21,2
5,28
44.
Div
isio
n of
pol
ynom
ials
by
Pp. 2
21-2
22P.
223
a po
lyno
mia
l..V
ritte
n E
x.1,
2,3,
5,6,
7,8,
9,11
,13,
15,1
6,26
,27,
28,3
5
SEE
IN
STR
UC
OR
. FO
R T
EST
- 47
-
UN
IT V
liSP
EC
IAL
PR
OD
UC
TS
AN
D F
AC
TO
RIN
GST
UD
EN
TA
SSIG
NM
EN
T S
HE
ET
ASS
IGN
IviL
NT
TO
PIC
RE
AD
ING
A S
SIG
Niv
.IE
N T
DA
TE
CO
MPL
ET
ED
4 .
Tac
tori
ng a
n in
tege
r in
toPp
. Z37
-239
P. 2
39pr
imes
Ora
l Ex.
i -22
P. 2
40W
ritte
n E
x.1,
2,5,
8,9,
11,1
7,19
,21,
23,2
4,26
, Z9
.C
omm
on m
onom
ial a
ndPp
. 241
-242
P. 2
4Zpo
lyn.
omia
l fac
tori
ngW
ritte
n E
x. 2
,3,5
,6,7
,8,1
0,11
,12,
13,1
4,15
,17,
19,2
0,21
,22
23,2
9,31
,32,
34,3
6
47.
Prod
uct o
f th
e su
m a
nd.
P. 2
45P.
245
diff
eren
ce o
f tw
o nu
mbe
rsO
ral E
x..1
,5,8
,9,1
1,12
,13:
15,1
6,17
,13
,19,
20,2
1...
.
48.
-FaC
tori
ng th
e di
ffer
ence
of
Pp. 2
46-2
47Pp
. 247
-248
two
squa
res
Wri
tten
Ex.
1,2,
4,5,
7,10
,11,
13,1
5,16
,21,
22,2
3,27
,29
=9.
Squa
ring
a b
inom
ial
Pp. 2
48-2
49Pp
. 249
-25G
Ora
l Ex.
1 , 3
, 5
, 4 ,
7 , 8
, 9 ,
1 0
,1
1 , 1
3 ,
1 5
,
16,2
1,22
.M
ultip
lyin
g bi
nom
ials
at
Pp. 2
53-2
54P.
254
sigh
tO
ral E
x.1,
2,3,
7,3,
9,13
,14,
15,1
6,11
,18
P. 2
54W
ritte
n E
x. 1
,2,3
,4 5
,6,7
,8,9
,10,
12 1
4 16
17
Zl
- 48
-
5
ASS
IGN
ME
NT
TO
PIC
RE
AD
ING
ASS
IGN
/viE
N T
DA
TE
CO
MPL
ET
ED
51.
Fact
orin
g th
e pr
oduc
t of
Pp. 2
55-2
56Pp
. 252
-253
bino
mia
l sum
s an
ddi
ffer
ence
Wri
tten
Ex.
3, 4
, 5, 6
, 11,
12,
21,
28
P. 2
56O
ral E
x.2,
5,7,
3,10
,13,
15,
18
P. 2
55W
ritte
n E
x.1,
2, 3
, 4, 5
,6, 7
,8, 9
, 11,
13, 1
5, 1
7, 1
8, 2
0,22
, 23
52.
Fact
orin
g th
e pr
oduc
t of
aPp
. 257
-258
P. 2
58bi
nom
ial s
um a
nd b
inom
ial
-Wri
tten
Ex.
2, 3
, 4, 5
,6,8
, 10,
11, 1
3,di
ffer
ence
15,1
6,11
,19,
21,2
0,24
53.
Fact
orin
g qu
adra
ticPp
. 259
-250
Pr*.
252
-253
trin
omia
lsW
ritte
n E
x.1,
8, 9
, 13,
15
P. 2
66W
ritte
n E
x.1,
2, 4
, 5,6
,7, 9
, 11,
12,
13,
14, 1
5, 1
6, 1
7, 1
8, 2
0
4.C
ombi
ning
sev
eral
type
s of
P. 2
51P.
253
fact
orin
gW
ritte
n E
x.24
, 25,
26,
30
P. 2
62W
ritte
n E
x.1,
3, 4
,5,6
,8, 1
0,1.
1,12
,14
, 15,
16,
18,
20,
22,
23,
25, 2
8, 2
9, 3
1, 3
3, 3
5
55.
Vio
rkin
g w
ith f
acto
rs w
hose
Pp. 2
63-2
64P.
264
prod
uct i
s ze
roW
ritte
n E
x.2,
4, 7
,8, 1
3, 1
4, 1
5, 1
7,13
,19
- 49
-
ASS
IGN
ME
NT
TO
PIC
RE
AD
ING
ASS
IGN
ME
NT
DA
TE
CO
MPL
ET
ED
56.
Solv
ing
equa
tions
by
Pp. 2
64-2
65P.
256
fact
orin
gPp
. 267
-269
Wri
tten
Ex.
1,3,
4,6,
7,8,
9,11
, la,
14,
16,1
7,19
,20,
22,2
3, a
4,2
6,27
,29,
30,3
1,33
,35
P. 2
69Pr
oble
ms
2,7,
19
57.
Add
itive
inve
rse
ofU
se th
e m
ultip
licat
ion
prop
erty
of
-1. p
olyn
omia
lsto
fin
d th
e ad
ditiv
e in
vers
e of
:1.
6x2.
4yb
3.-7
ad4.
-9xy
z5.
x-7
. o .
x+5
7.2y
-58.
3y+
79.
-5y+
910
.-6
x-4
11.
63/ (
-5)
12.
4x +
5x-1
13.
7x2+
5x+
9
SEE
INST
RU
CIT
OR
FOR
TE
ST
.FR
AC
TIO
NS
STU
DE
NT
ASS
IGN
ME
NT
SH
EE
T
ASS
IGN
ME
NT
TO
PIC
RE
AD
ING
ASS
IGN
ME
NT
DA
TE
CO
MPL
ET
ED
58.
Res
tric
ting
the
repl
acem
ent
Pp. 2
81-2
82P.
282
set o
f th
e va
riab
leW
ritte
n E
x.1,
2, 4
, 7, 8
, 9, 1
4, 1
5, 1
7O
ral E
x.1,
2, 3
, 4, 6
, 8, 1
1
59.
Red
ucin
g fr
actio
nsPp
. 283
-284
Pp. 2
84-2
85W
ritte
n E
x.1,
2,3
,4, 5
,7,8
, 9, 1
1, 1
2,14
, 15,
17,
18,
20,
24
60.
Rat
ioPp
. 286
-287
P. 2
87O
ral E
x.1,
3, 5
, 7, 9
, 13,
15
1:1p
. 287
-288
Wri
tten
Ex.
5, 9
Pp. 2
88-2
89Pr
oble
ms
3, 6
, 8
61.
Mul
tiplic
atio
n of
fra
ctio
nsPp
. 292
-293
P. 2
93O
ral E
x.1,
3, 5
, 7, 9
, 11,
13,
18,
20,2
7,29
Pp. 2
93-2
94W
ritte
n E
x.1,
2, 4
, 5, 7
, 9, 1
1, 1
4, 1
5, 1
7,18
,20,
21,2
2,25
,26,
31,3
5,36
62.
Div
isio
n of
fra
ctio
nsPp
. 295
-296
Pp. 2
95-2
96W
ritte
n E
x.1,
3, 4
, 5, 6
, 9, 1
0, 1
1, 1
2, 1
3,14
, 15,
16,
19, 2
0, 2
3, 2
4, 2
7
- 51
-
ASS
IGN
ME
NT
TO
PIC
RE
AD
ING
ASS
IGN
ME
NT
DA
TE
CO
MPL
ET
ED
63.
Mul
tiplic
atio
n an
d di
visi
onPp
. 296
-297
Pp. 2
96-2
97of
fra
ctio
nsW
ritte
n E
x.1,
3, 5
, 8, 1
1, 1
4, 1
5, 2
0Pp
. 168
-169
Prob
lem
s1,
4, 6
, 11,
17
SEE
IN
STR
UC
TO
RFO
R T
EST
64.
Add
ition
and
sub
trac
tion
ofPp
. 297
-298
Pp. 2
98-2
99fr
actio
ns w
ith e
qual
.de
nom
inat
ors
Wri
tten
Ex.
1, 2
, 3, 4
, 5, 6
, 8, 9
, 10,
12,
13,
17, 1
9
5.A
dditi
on a
nd s
ubtr
actio
n of
Pp. 2
99-3
01P.
300
frac
tions
with
une
qual
Ora
l Ex.
1,3,
4,6
,7, 1
3, 1
5,17
,19
deno
min
ator
sPp
. 301
-302
Wri
tten
Ex.
1,2,
3, 4
,6,8
, 9, 1
0, 1
1, 1
3,14
, 15,
17,
20,
22,
23,
24,
25,
27,3
0,31
.M
ixed
exp
ress
ions
Pp. 3
02-3
03P.
303
Wri
tten
Ex.
2, 4
, 7, 9
, 11,
13,
15
.C
ompl
ex f
ract
ions
Pp. 3
04-3
05P.
305
Wri
tten
Ex.
1,3,
4, 5
, 7, 9
, 10,
13,
15
.O
pen
sent
ence
s w
ithPp
. 306
-307
P. 3
07fr
actio
nal c
oeff
icie
nts
ritte
n E
x.1,
3, 5
, 8, 9
, 12,
14,
16,
17,
21
9.Fr
actio
nal e
quat
ions
Pp. 3
12-3
13Pp
. 313
-314
ritte
n E
x.1,
3, 5
,8, 9
, 11,
14,
15,
17,
25
SEE
IN
STR
UC
TO
RFO
R T
EST
- 52
-
UN
IT I
XG
RA
PHS
OF
EQ
UA
TIO
NS
STU
DE
NT
ASS
IGN
ME
NT
SH
EE
T
ASS
IGN
ME
NT
TO
PIC
RE
AD
ING
ASS
IGN
ME
NT
DA
TE
CO
MPL
ET
ED
70.
Ope
n se
nten
ces
in 2
Pp. 3
33-3
35P.
335
vari
able
sO
ral E
x. A
ll pr
oble
ms
71.
Coo
rdin
ates
in th
e pl
ane
Pp. 3
37-3
38P.
339
Ora
l Ex.
2,4
,6,7
,9,1
1,13
,15,
17,2
1-32
P. 3
40W
ritte
n E
x.1,
3,4,
5,7,
11,1
272
.G
raph
ing
of li
near
equ
atio
nPp
. 340
-341
Pp. 3
41-3
42in
2 v
aria
bles
Ora
l Ex.
1,2
,3,5
,8,1
0,11
,13,
14,1
5,16
,18,
28,3
0P.
342
Wri
tten
Ex.
1,3,
5,6,
7,10
,11,
13,1
5,17
Gra
sL
i:1.
6.y
= 3
2.x
+ 3
= 0
7.
y =
-8
3 .
x =
-4
8.y
+6
= 0
4.x
- 5
= 0
9.y
- 4
= 0
5.x
= 0
73.
Slop
e of
a li
nePp
. 343
-344
Pp. 3
44-3
45O
ral E
x.1,
2,3,
4,5,
6,7,
8,9,
11,1
3,16
Pp. 3
45-3
46W
ritte
n E
x.1,
3,5,
638,
9,10
,11,
12SE
E I
NST
RU
CR
FO
R T
EST
- 53
-
ASS
IGN
ME
NT
TO
PIC
RE
AD
ING
ASS
IGN
ME
NT
DA
TE
CO
MPL
ET
ED
74.
Slop
e-in
terc
ept f
orm
of
aPp
. 34S
-348
P. 3
48lin
ear
equa
tion
Ora
l Ex.
1,3
, 5,6
,7, 1
0,11
, 14,
15
P. 3
48W
ritte
n E
x.1,
3, 5
,7,8
, 10,
11,
12, 1
3, 1
5
75.
Det
erm
inin
g eq
uatio
ns o
f a
P. 3
49P.
350
line
give
n po
int -
slo
pe a
ndpo
int -
poi
ntW
ritte
n E
x.1,
2, 4
, 5, 6
, 9, 1
0, 1
2, 1
3, 1
4,16
, 18
76.
Gra
ph in
equa
litie
s in
two
Pp. 3
50-3
52P.
352
vari
able
sO
ral E
x.1,
3,7,
8, 9
, 12,
13,
14,
15
P. 3
52W
ritte
n E
x.1,
3, 5
,6,7
, 10,
11
Gra
ph: y
=x2
and
y =
'lir
77.
Solu
tion
of s
imul
tane
ous
Pp. 3
67-3
69P.
370
equa
tions
- g
raph
ic m
etho
dW
ritte
n E
x.1,
3, 5
, 9
78.
Solu
tion
of s
imul
tane
ous
Pp. 3
70-3
71P.
372
equa
tions
- a
dditi
onW
ritte
n E
x. 2
.3, 6
,8, 1
4su
btra
ctio
n m
etho
d.
79.
Solu
tion
of s
imul
tane
ous
Pp. 3
74-3
75P.
376
equa
tions
. m
ultip
licat
ion
in th
e ad
ditio
n-su
btra
ctio
nm
oth.
..%d
Wri
tten
Ex.
1,3,
6,10
ASS
IGN
ME
NT
TO
PIC
RE
AD
ING
ASS
IGN
ME
NT
DA
TE
CO
MPL
ET
ED
80. .
Solu
tion
of s
imul
tane
ous
equa
tions
- s
ubst
itutio
nm
etho
d
Solu
tion
of s
imul
tane
ous
equa
tions
- d
eter
min
ants
P. 3
78
Exp
lana
tion
byin
stru
ctor
SEE
IN
STR
UC
TO
RP. 3
78W
ritte
n E
x.1,
3, 4
,6,
10 dete
rmin
ants
:4
- II
06
1 - 2-
2
14
dete
rmin
ants
)
1
to:
Eva
luat
e
1.1 1
2. 3. P. 3
72W
ritte
n
the
3 5
12[
1 -5
11
14
6
-1 -
26
-3 Ex.
follo
win
g
4.
1
5.
i
(Cha
nge
dire
ctio
nsSo
lve
by5,
7,11
,12
FOR
TE
ST
UN
IT X
TH
E.R
EA
L N
UM
BE
RS
STU
DE
NT
ASS
IGN
ME
NT
SH
EE
T
ASS
IGN
ME
NT
TO
PIC
RE
AD
ING
ASS
IGN
ME
NT
DA
TE
CO
MPL
ET
ED
82.
Nat
ure
of r
atio
nal n
umbe
rsPp
. 397
-398
P. 3
99O
ral E
x.2,
3, 5
,6, 1
0, 1
2, 1
4, 1
5, 1
6, 1
7,19
,22,
23P.
400
Wri
tten
Ex.
15, 1
6, 2
0
83..
Dec
imal
for
m o
f ra
tiona
lPp
. 400
-402
P. 4
03nu
mbe
rsW
ritte
n E
x.1,
4, 5
,7, 1
1, 1
3, 1
7, 1
8
84.
Roo
ts o
f nu
mbe
rsPp
. 403
-405
P. 4
05O
ral E
x.I,
2,3
, 4, 5
,7,8
, 13,
14,
17,
18:
23,2
4,27
,28
Pp. 4
05-4
06N
ritte
n E
x.1,
2, 3
,7
85.
Prop
ertie
s of
irra
tiona
lP.
407
P. 4
10nu
mbe
rsO
ral E
x.1,
3, 4
,6,7
,8, 1
1, 1
3,14
, 15,
11,1
8
86.
Prod
uct a
nd q
uotie
ntPp
. 414
-415
P. 4
15pr
oper
ties
of r
adic
als
Ora
l Ex.
1, 2
, 3, 4
, 5, 9
, 11,
13,
14,
/5,
17-3
1,33
-36
Pp. 4
15-4
16W
ritte
n E
x.1,
3-7
, 10-
13,
16,
18,
19,
23,
26, 2
8, 2
9:30
SEE
IN
STR
UC
.O
R F
OR
TE
ST
- 56
-
ASS
IGN
ME
NT
TO
PIC
RE
AD
ING
ASS
IGN
ME
NT
DA
TE
CO
MPL
ET
ED
87.
Add
ition
and
sub
trac
tion
ofra
dica
ls
8M
ultip
licat
ion
of b
inom
ials
cont
aini
ng r
adic
als
9.R
atio
naliz
ing
deno
min
ator
sco
ntai
ning
rad
ical
s
Solu
tions
of
radi
cal
equa
tions
Pp. 4
17-4
18
Pp. 4
19-4
20
P. 4
20 T
opE
xam
ple
3
P. 4
21
P. 4
18O
ral E
x.1,
2,4,
5,7,
9.1
1,12
,15
Pp. 4
18-4
19W
ritte
n E
x.1,
2,4,
5,6,
8 -1
1, 1
5
P. 4
20W
ritte
n E
x.1,
4,5
,7,8
, 9, 1
0,1_
2,13
, 15
P. 4
20W
ritte
n E
x.17
, 18,
19,
21,
24
P. 4
22W
ritte
n E
. 1,3
,5,6
, 9, 1
3, 1
5,17
,20
ISE
E I
NST
1.2.
UC
OR
FO
R T
EST
UN
IT X
IR
EL
AT
ION
S, F
UN
CT
ION
S A
ND
VA
RIA
TIO
NST
UD
EN
TA
SSIG
NM
EN
T S
HE
ET
ASS
IGN
ME
NT
TO
PIC
RE
AD
ING
ASS
IGN
ME
NT
.
DA
TE
CO
MPL
ET
ED
9R
elat
ions
2.
Func
tions
Pp. 4
35-4
36
Pp. 4
38-4
39
.D
irec
t var
iatio
n an
dPp
. 442
-44
3pr
opor
tion
.In
vers
e va
riat
ion
Pp. 4
47-4
49
SEE
IN
STR
UC
T
P. 4
37O
ral E
x.13
, 14,
15,
16,
17,
18
P. 4
37W
ritte
n E
x.1,
2,6
,7,8
, 9, 1
1, 1
2
P. 4
40O
ral E
x.1-
15Pp
. 441
-442
Wri
tten
Ex.
1, 3
, 5, 9
, 14,
15,
17
G r
a 2
1 :
x> 0
y=
Pp. 4
44-4
45O
ral E
x.11
, 12,
13,
16, 1
8,22
-29
P. 4
45W
ritte
n E
x.1,
2, 3
, 4, 7
,8,
11, 1
5Pp
. 446
-447
Prob
lem
s1,
2, 6
, 7, 9
Pp. 4
50-4
51W
ritte
n E
x.1,
2, 4
,5, 7
P. 4
51Pr
oble
ms
1, 2
, 3, 5
,10
OR
FO
R. T
EST
- 58
-
(0 .
PRO
BL
EM
S U
NIT
STU
DE
NT
ASS
IGN
ME
NT
SH
EE
T
ASS
IGN
ME
NT
TO
PIC
Tra
nsla
.ting
Eng
lish
sse
nten
ces
into
alg
ebra
icse
nten
ces.
Solv
ing
prob
lem
s w
ithop
en s
ente
nces
97.
Num
ber
prob
lem
s
98.
Prob
lem
s w
ith d
irec
ted
num
bers
99 =
Dif
fere
nces
of
dire
cted
num
bers
Wor
k pr
nble
ms
RE
AD
ING
P. 5
1
ASS
IGN
/viE
NT
DA
TE
CO
MPL
ET
ED
Pp. 5
6-58
Pp. 1
16-1
17
Pp. 3
14-3
15
P. 5
4W
ritte
n E
x.1,
6,7
,8, 1
2, 1
3, 1
6, 1
7-20
P. 5
5Pr
oble
ms
3, 6
, 9, 1
1, 1
2, 1
4, 1
7
P. 5
8O
ral E
x.1-
12P.
51-
Prob
lem
s 1,
5,7
,9, 1
0, 1
7,20
, 23
P. 8
9Pr
oble
ms
1, 3
, 4, 7
, 10,
12,
13,
18,
20,
21
P. 9
4Pr
oble
ms
3, 5
, 7, 1
1, 1
2, 1
5
P. 1
19Pr
oble
ms
1, 4
, 6, 1
2P.
128
Prob
lem
s i,
5, 6
, 9
P. 1
32Pr
oble
ms
1, 3
, 5, 6
, 10,
11
Pp. 3
15-3
16Pr
oble
ms
1, 4
, 5, 7
, 8
- 59
-
DIAGNOSTIC TESTS
DIAGNCSTIC TEST
DIRECTIC NS: Do not write on this test booklet. Place all answers on theanswer sheet provided to you. Do not spend too much time on any oneproblem.
1. TRUE or FALSE: 6E {even numbers greater than 10}.2. List all members of the set of even numbers between 1 and 11.3. Write a rule describing all members in the set {a, e, i, o, u }.4. TRUE or FALSE: There is a one-to-one correspondence between the
set {1, 9, 11} and the set {even numbers between 3 and 9}.
Which one of the following sets is infinite? Place the letter beforethe correct answer on your sheet.A. {people on earth}B. {sand grains on a beach}C. {states in the Union}D. {whole numbers greater than 101
Which one of the following symbols represents the null or emptyset? Place the letter of the correct answer on your sheet.
7. How many Members are there in the ;set Ian people in the room over10 feet tall} ?
. Find all the f.:tets in the list whiCh are subsets of {a, b, 1; 2}. Place"the letter or letters of the correct :answers on your answer sheet..
A._ :fa, 1/ 13:, (b)E: 0:
F. {a,
IIMIII111m,
7,..
10. The graphs of the numbers 1, 2, 1,line below.
1A. Which point is the graph of the number
2?
23 5, and are given on the number
3
B. What is the coordinate of D?C. What would be the coordinate of a point halfway between C and E?
D B E F C
01
23 52 3
For problems 11 through 14, indicate whether thebe replaced by (a) the = symbol, (b) the < symbol,make each statement true. Place the letter of theanswer sheet.
16+9 ?21=4 ?.
15+21.?
19-3 ?
5x5.
3x5
0.
3+ 7
question mark shouldor (c) the > symbol tocorrect answer on the
In problems 15 to 18, ell which of the following graphs represents thegiVen set.
15. {1, 3.5}4
0 1 3 4 5
B111.1 a-
1 3 5
D..
{All numbers between three and five)
B.0 1 2 3 4 5 6
C. S= t5=1:;0 1 2 3 4 5 6
D.
0 1 2 3 4 5 6
17: {A11 numbers between 0 and 1, including 0 and 1}
A.0 1
. B. fiwegnoti,
1 2
3
3
1
4
18. {All nuriibe'rs greater than 4):
0
N.
2
--4~
3 4
=s2. 3 4
0 1 2
I
3 4
-0 1 2 3 4
Calculate the value of each number phrase., Placethe correct solution on your answer sheet.
19. (164) 7. 2
20. 13(13,9) - 9(13-9)21. 236"
:22. [6- (4 -i-2)1* 3
23. 6 9 - 4x2 + 10 2: .
A -4.
DIAGNOSTIC TEST
NAME
TEACHER
SCORE
COMMENTS
3.
SECTION
DATE
PERIOD
20. ,21.
22.
23.
Acceptable Score 1623
TEACHER'S ANSWER KEY
DIAGNOSTIC TEST First Year Algebra
1. True
2. 12,4,5,8,101
3. {vowels}
4. True
(1) 13. C (4)
(1) 14. C (4)
(1) 15. A (6)
(I) 16. C (6)
(1) 17. S (6)
(1) 13. D (6)
(1) 19. 10 (7)
(2)' 20. 16
21.
APPENDIX B
ACHIEVEMENT TESTS
FOR
A SELF-PACING PROGRAM IN ALGEBRA
VOLUME I
UNIT I Sets, Sentences and the Number Line PART I
DIRECTIONS: Do NOT write on this test booklet. Place all answerson the answer sheet provided to you. Do not spend too much time on anyone problem.
1. TRUE or FALSE: 54- {even numbers greater than 10}2. List all of the members of the set of odd numbers between 5 and 13.3. Write a rule describiag all the members in the set {a, e, i, o, u }.4. TRUE or FALSE: There is a one-to-one correspondence between
the set { 1, 9, 10} and the set {odd numbers betvrnen 4 and 10}.5. Which one of the following sets is infinite? Place the letter of the
correct answer on your answer sheet.A. {atoms in the head of a pin}B. {brilliant algebra teachers}C. {whole numbers greater than 15}D. {nations in the world}
6. Which one of the following symbols represents the null or empty set?Place the letter of the correct answer on your answer sheet.A. 4,
B. {0}
C. {4)}
D. 0
7. How many members are there in the set {all people who have el6 renheads} ?
3. Find all the sets in the list which are subsets of { 1, 2, b, c }. Placethe letter or letters of the correct answer on your answer sheet.A. {a, 1} D. {b}
B. {a, c} E. 4,
C. {a, b, 2} F. {b, 1, 2, c}
9. Write all the subsets of the set {0, 1}.
8-2
UNIT I Sets, Sentences and the Number Line
NAME SECTION
TEACHER DATE
SCORE PERIOD
1.
2.
3.
4.
5.
6.
7.
3.
9.
B-3
79
PART I
UNIT I 3e.ts, Sen'ences and the Number Line PART IITEST A
DIRECTIONS: Do NOT write on this test booklet. Do all scratch workon the paper provided to you. Place correct answer in the appropriateblank of your answer sheet. Do not spend too much time on any oneproblem.
I. Identify each of the following as an (A) equation, (B) inequality, or(C) neither. Write the letter of the correct answer in the space provided.
1. 7+5 = 12
2. 8-3 = 143. 27 + 5 # 1?4. 63 + 11 > 45. 3 - 6 > 96. 9+ 3 x 27. 6 + 5 <?
II. Write TRUE or FALSE in the appropriate space.1. 13+ 3 = 13+32. 3 +4x5 = 60
3. 7+ 12>4x2+ 5
4. 6x0<3+ 3
5. .5x12<15-9
GO ON TO THE NEXT PAGE
B74
80
3. {Ail numbers between 0 and 4, including 0 and 4)A.
4) 4;0
(I,1 2
B. 0--0 1 2
C.
0 1 2
D.
(I)3 4
3 4
3 4
0 1 2 3 4
4. {All numbers greater than 2}
1.
A.
B.
C.
D.
4
0 1 2 3 4
0 1 2 3 4
0 1 2 3 4
0 1 2 3 4
VI. Calculate the value of each number phrase. Place your answer on thesheet. provided.
(16-10)-5
2. 13(11-3)-3(11.-8)
3. 16-4 + 2x4
4. [3-(3+2)Ix 45. 6+3 - 3x2 + 10+5
B -5
81
III. The graphs of the numbers 0, 1, 2, 3, 3?, 4 are on the given numberline below.
A D B E F C1
0 1 2 3 3-2
4
1. Which point is the graph of the number 2?2. What is the coordinate of F?3. What would be the coordinate of the point halfway between A and B?
IV. Indicate whether the ? should be replaced by (A).the symbol =, (B) the< symbol or (C) the > symbol to make each statement true.1. 16+4 ? 3x7
2. 21- 6 ? 3x5
3. 5+ 13 ? 04. 19 -5 ? 2+3
V. Tell which of the following graphs represents the given set.1. {1,
A.
3, 5}
0 1. 2 3 4 5
B.>-I #
0 1 2 3 4 5
C.
0 1 2 3 4 5
D.
1 2 3 4 5
2. {All numbers between 2 and 3}A.
B.
C.
D.
0 1 2 3
0 1 2 3
0 1. 2 3
UNIT I. Sets, Sentences and the Number Line PART IITEST B
DIRECTIONS: Do NOT write on the test booklet. Place all answers onthe paper provided.
I. Identify each of the following as an (A) equation, (B) inequality, or(C) neither.1. 7 +6 = 13
2. 3-4 = 43. 27+6 = 76
4. 76+ 96>67
5. 6-4<7
6. 8+5-6
7. 9-5<5-3
II. Write TRUE or FALSE in the appropriate space.1. 3+ 14 = 1
2. 4+5x8 = 443. 5+ 9>7+ 9
4. 9-6<3+ 4
5. . 4x9>2+ 0
III. The graphs of the numbers 0,1,2, 3, 3i-, 4 are on the given number linebelow.
D A E H K L
41
0 1 2 3 3-2
4
1. Which point is the graph of 3?2. What is the coordinate of H?3. What is the coordinate of the point halfway between A and H?
B-7
83
4. {All numbersA.
greater than 4)
(-41mallai41.$i;.
0 1 2 3 4 5
0 1 2 3 4 5
C.
0 1 2 3 4 5
D.
0 1 2 3 4 5
VI. Calculate the value of each number phrase. Place your answer on thesheet provided.I. 26-(10+ 4)
2. 12(11-8)-6(11-S)
3. 20-5x2+ 6
4. 16-44-2x4
5. 16+ 5-4x5+ 204-5
B -8
84
IV. Indicate whether the ? should be replaced by (A) the symbol =, (B) theLimo. < symbol, or (C) the > symbol.
1. 17+4 ? 3x52. 29-0 ? 5+7i
3. 6+6 ? 3x4
4. 19-5 ? 2+3
V. Tell which of the following graphs represent the given set.1. {2, 4}
A.
0 1
B. 4
0 1
C.
0 1
D.
0 1
2
2
2
(D-2
2. {All numbersA.
13.
between 3 and 5}
0 1 2
0 1 2
C.
0 1 2
D.
0 1 2
--3 4 5
3 4 5
3 4 5
17..
3 4
0
5
a--3 4 5
3 4 5
3 4 5
3 4 5
3. {All numbers between 4 and 6 including 4 and 6}A.
B.
C.
D.
0 1
2 3i,6 7
2 3 4 5
- 9
6
UNIT I
NAME
TEACHER
SCORE
Sets, Sentences and the Number Line PART II A B C D
SECTION
DATE
PERIOD
I. - 1. VI.- 1.
.0.11/MOMOI.I2.
3. 3.
4. 4.
5. 5.
6.
7.
II. -1.2.
3.
4.
5.
III. - 1.
2.
3.
IV. - 1.
2.
3.
4.
V. - 1.
2.
4.
Unit II VARIABLES Test A
DIRECTIONS: Do not write on this test booklet. Do all scratch work onthe paper provided to you. Place the correct answer in the appropriateblank of your answer sheet. Do not spend too much time on any one problem.
Choose a word from the following list that correctly completes each numberedblank in the paragraph. Write the letter of the correct answer on the answersheet.
A. CONSTANT B. BASE C. POWER D. REPLACEMENT SETE. TERM F. VARIABLE G. EXPONENT H. COEFFICIENTI. FACTOR
Let A = { 1, 2, 3, 4} and consider the expression x2. If x can be replacedonly with numerals of set A, A is called the (1) of x.Since x is a symbol which is to be replaced with the Tmes of numbers, xis called a (n) (2) . In the expression x , x is called the
(3) and 2 is called the (4) . In theexpression 32y2, 32 is called the (5) of yZ. 32 is alsocalled a (n) (6) of the entire expression. In the expression10x + y, 10x and y are called (7) of the expression.
8. The expression 15x2y + '3xy2 + 7x - 2y :las how many terms?9. The expression (a-b)(a+b)(b-a) has how many factors?
310. Which expression in the following list is equivalent to i-?
3A. 71a
B.3a4
C. Neither A or B
D. Both A and B
11. Which expression in the following list is equivalent to 3 times a?
A. 3a
B. 3 aC. (3)(a)
D. None of the aboveE. A, B and C
B-11
87
12. If b= 3, the value of13. If b= 3, the value of
14.
15.
16.
2b2 is what?(2b)
2 is what?
If a= 1, b= 2, and c= 3 , evaluate each of the expressions fromnumber 14 to number 16.
3a + b2
(3a + b)2
(c + 2)(c + 2b2)
Write YES or NO to indicate whether or not the expression on the left isa correct translation of the English phrase on the right in problems 17to
17.
18.
19.
20.
21.
22.
23.
23.
n + 4a - 85bx3
2t - 15(w + 2)
2 - b
a number increased by 4a number diminished by 85 more than a numberone-third of a numberone less than twice a number2 more than five times a number2 less than some number
Write an algebraic expression for each English expression in problems24 through 32 Use the variable suggested.
24.
25.
26.
27.
28.
29.
30.
31.
32.
the sum of x and 57 less than a5 diminished by n
7 times cthe sum of 6 and two times d2 less than three times f5 times the sum of in and 22 times w is greater than 3A number x increased by 7 is 15.
Write as a power33. b. b. b
34. 2. Z. 2
35. (6a) (6a)
36. COMPLETION: The value of 0 to any positive power is
37. COMPLETION: The value of 1 to any positive power is
Perform the indicated operations in problems 38 - 42.
38.
39.
42 =
25 =
40. (4a)(2a) =
41. (3a) 3=
42. (9x)2 =
B-13
R9
Unit II VARIABLES Test B
DIRECTIONS: Do not write on this test booklet. Do all scratch work onthe paper provided to you. Place the correct answer in the appropriateblank on your answer sheet. Do not spend too much time on any one problem.
Choose a word from the following list that correctly completes each numberedblank in the paragraph. Write the letter of the correct answer on the answersheet.
A. CONSTANT B. BASE C. POWER D. REPLACEMENT SET
E. TERM F. VARIABLE G. EXPONENT H. COEFFICIENT
I. FACTOR
Let A = {3, 5, 6, 7,) and consider the expression x3. If x can be replacedwith only numerals of the set A, A is called the (1) of x.Since x is a symbol which is to be replaced with the :names of numbers, xis called a (n) (2) . In the expression x3, y is called the
(3) and 3 is called the In the expression16-2-76y is called (5) of yZ. 16 is also called a (n)
(6) of the entire expression. In the expression 10y+x, lOyand x are called (7) of the expression.8. The expression 7x 2y+5xy 2+ 3x+ y has how many terms?9. The expression (x-y)(x+y)(y-x) has how many factors?
10. Which expression in the following list is equivalent to 3a?5
3
aA. 5a C. Neither A or B
B.3a
D. Both A and B5
11. Which expression in the following list is equivalent to 4 times a?A. 4a
B. (4)(a)
C. 4.a
D. All of the above2
12. If b= 2, the value of 4b is what?
13. If b= 2, the value of (4b)2 is what?If a= 2, b= 1 and c= 3, evaluate each of the expressions in problems 14-16.
90B-14
14. 2a +b2
15. (2a +b)2
16. (b+2)(b+c2)
Write YES or NO to indicate whether or not the expression on the left is acorrect translation of the English phrase on the right in problems 17-23.
17. n+ 2
18. a +9
19. lb20. 421. Zy-1
22. 3(w+ 2)
23. 7-b
a number increased by 2a number diminished by 8
7 more than a numberone - fourth of a number
one less than twice a numbertwo more than three times a number7 less than some number
Write an algebraic expression for each English expression in problems 24-32. Use the variable suggested.
24. the sum of x and 925. 12 less than a
26. 11 diminished by n
27. 8 times c
28. the sum of 5 and three times d29. 1 more than three times f30. 4 times the sum of h and 3
31. 3 times w is less than 232. a number y decreased by 10 is 26.
Write as a Power
33. b. b. b
34. 2. 2. 2. 2
35. (6a)(6a)
36. COMPLETION: The value of 0 to any positive power is
37. COMPLETION: The value of 1 to any positive power is
B-15
91
Perform the indicated operations in problems 38-42.
38. 42=
39. 25=
40. (4a)(2a) =
41. (3a)3
=
42.2
(9x) =
UNIT II VARIABLES TEST C
DIRECTIONS: Do not write on this test booklet. Do all scratch work on thepaper provided to you. Place the correct answer in the appropriate blank ofyour answer sheet. Do not spend too much time on any one problem.
Cn your answer sheet write the letter of the word which correctly completeseach sentence of the paragraph.A. CONSTANT B. BASE C. POWER D. REPLACEMENT SETE. TERM F. VARIABLE G. EXPONENT H. COEFFICIENTI. FACTO. R
Let A = {2, 4, 5, 3} and consider the expression y2. I.f y can be replacedonly with the numerals of set A, A is called the (1) of y.Since y is a symbol which is to be replaced with the names of numbers, y iscalled a (n) (2) . In the expression y2, y is called the
(3) and 2 is called the (4) . In the expression20y2, 20 is called the (5) of y2. 20 is also called a (n)
(6) of the entire expression. In the expression 3x+ y, 3xand y are called (7) of the expression.3. The expression 10x2y + 2xy2 - 6x has how many terms?9. The expression (b-a)(a-f b) (a-b)c has how many factors?
210. Which expression in the following is equivalent to iR ?
A. 2-3R C. Neither A or B
B.3
2RD. Both A and B
11. Which expression in the following list is equivalent to five times w.
A. 5w
B. 5 wC. (5)(w)
D. None of the above
E. A, B and C
12. If b= 2, the value13. If b= 2, the value
If a= 1, b= 2, and c= 3, evaluate each of the expressions from number14-16.
14. 4a + 132
15. (3a+ 2b) 2
16. (c+3)(2b2+c)
of 5b 2 is what?of (5b)2 is what?
t
Write YES or NO to indicate whether or not the expression on thecorrect translation
17. y + 61
a8.
219. 2,x-1
20. B -4
21. 5(x+3)
22. 2-R
23. ION
left is aof the phrase on the right in problems 17-23.
a number increased by 6one-half of a numberone less than twice a numbera number diminished by 43 more than five time s a number2 less than some number10 more than a number
Write an algebraic express for each English expression in problems 24through 32. Use the variable suggested.
24. the sum of x and 225. 5 less than N26. 2 diminished by x27. 17 times b28. the sum of 4 and three times y2 9. 1 less than two times S30. 3 times the sum of a and 531. 2 times N is greater than 532. a number c increased by 5 is 15
B-18
94
Write as a power.
33. x. x
34. 3. 3. 3. 3. 3
35. (5b)(5b)
36. COMPLETION: The value of 0 to any positive power is37. COMPLETION: The value of 1 to any positive power is
Perform the indicated operations in problems 38-42.
33. 32=
39. 25 =
40. (3b)(4b) =
41. (2b)2=
42. (51)3 =
B -19
95
Unit II VARIABLES Test D
DIRECTIONS: Do not write on this test booklet. Do all scratch work on thepaper provided to you. Place the correct answer in the appropriate blankon your answer sheet. Do not spend too much time on any one problem.
Choose a word from the following list that correctly completes each numberedblank in the paragraph. Write the letter of the correct answer on theanswer sheet.
A. CONSTANT 13. PCWER C. TERM D. FACTORE. EXPONENT F. COEFFICIENT G. VARIABLE H. BASE
I. REPLACEMENT SET
Let A = { 1, 2, 4, 5} and consider the expression y2. If y can be replacedwith only numerals of the set A, A is called the (1) of y. Sincey is a symbol which is to be replaced with theznames of numbers, y is calleda (n) (2) . In the expression y , y is called the (3)and 2 is called the (4) . In the expression 14y2, 14 is calledthe (5) of y2. 14 is also called a (n) (6) of theentire expression. In the expression 14y+ 2x, 14y and 2x are called
(7) of the expression.
8. The expression 4x2y+ 2xy2+3x+ y has how many terms?
9. The expression (x-4)(4-x)(4+x) has how many factors?2
10. Which expression in the following list is equivalent to 3a?A. 2a C. Neither A or B
3
B. 23a D. Both A and B
11. Which expression in the following list is equivalent to 6 times b?
A. 6b
B. 6b
C. (6)(b)
D. None of the above
E. A, 13 and C
/3.-20
12. If b= 2, the value of 3b2 is what?13. If b= 2, the value of (3b) 2 is what?
If a= 1, b= 2, and c= 3, evaluate each of the expressions in problems14-16.
14. 2a +b2
15. (2a+ 3b)2
16. (c2+b)(2 +a).
Write YES or NO to indicate whether or not the expression on the left is acorrect translation of the English phrase on the right in problems 17-23.
17. y + 3 a number increased by 318. 6b 6 more than a number
19.5
one-fifth of a number
20. y + 5 a number diminished by 521. 3y-1 one more than three times a number22. 6(w+ 5 ) six more than a number increased by 523. 6-y y less than 6
Write an algebraic expression for each English expression in problems24-32.
24. the sum of y and 625. 8 less than m26. 12 decreased by y27. 7 times d23. the sum of 4 and seven times x29. 1 less than three times y30. 7 times the sum of h and 431. 4 times v is greater than 632. a number m increased by 21 is 43
B-21
qj
Write as a power.
33. b b. b. b
34. 4. 4. 4
35. (7a)(7a)
36. COMPLETION: The value of 1 to any positive power is
37. COMPLETION: The value of 0 to any positive power is
Perform the indicated operations in problems 38-42.
33. 62=
39. 34 =
40. (4a)(3a) =
41. (2a)3
=
42. (7x)2 =
B-22
98
UNIT II Variables A B C D
NAME SECTION
TEACHER DATE
SC ORE PERIOD
1. 28.
2. 29.
3. 30.
4. 31.
5. 32.
6. 33.
7. 34.
8. 35.
9 36.
10. 37.
11. 38.
12. 39.
13. 40.
14. 41.
15. 42.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27. 99
Unit III Non-Negative Numbers of Arithmetic Test A
DIRECTICNS: Do not write on this test booklet. Place all answers on theanswer sheet. Do all scratch work on the paper provided to you. Do notspend too much time on any one problem.
COMPLETION:
1. The additive identity element is2. The multiplicative identity element is3. By the transitive property of equality, if b= a+ 2 and a+ 2= R, then
4. has no reciprocal.5. If x is the multiplicative inverse zf y, then (x)(y) =
In problems 6-11, write the answers for each problem. If the groupof symbols has no meaning, write "no meaning" on the sheet.
6. (16)(1)
7. 15. 0
63.
1
09.
5
10.
11.
7
000
Simplify the following expressions.12. 2(3y)
113.
2(12RS)
14. (4x)(9y)
In problems 15-17, tell whether the statement is TRUE or FALSE.15. 10, 1) is closed under the operation of addition.16. {0, 1) is closed under the operation of multiplication.17. The set of odd numbers is closed under the operation of multiplication.
B-24
103
In problems 13-22, write the letter of the property which is illustrated bythe example below.
A. Reflexive Property of EqualityB. Symmetric Property of EqualityC. Transitive Property of EqualityD. None of these
13. If 3 = 9-1, then 9-1 = 3.19. 4(3. 2) = (4. 3)2
20. 5 = 5
21. If 4-1 = 3 and 3 = 2+1, then 4-1 = 2+122. If 4+2 = 6, then 6 = 4+2
In problems 23-27, write the letter of the property which is illustrated bythe example below.
A. Commutative Property of AdditionB. Associative Property of AdditionC. Commutative Property of MultiplicationD. Associative Property of MultiplicationE. Distributive Property of Multiplication over Addition
23. 5(3 +2) = 5. 3 + 5. 2
24. 7+9 = 9+7
25. 3(2n) = (3. 2)n, for all numbers n26. 5+(4+1) = (5+4)+1
27. 3+(2+7) = (2+7)+3
In problems 28-32, write the letter of the property which is illustrated bythe example below.
A. Add!'..2.ve Property of Zero
B. Multiplicative Property of ZeroC. Multiplicative Property of OneD. None of these
23. 5. 0 = 0
29. (9. 3) +0 = 9. 3
30. 12+ 1 = 13
31. 16.1 = 16
32. 0. 14 = 14101
B-25
Write the reciprocal of:33.
3
34. 2
35. 1
36. Which term is similar to 6a? Write the letter of the correct answeron the answer sheet.A. Gab
B. 4a
C. 6b
D. 6
E. None of these
In problems 37-40 combine by adding or subtracting similar terms.37. 5a+7a
33. 12q-4q+1 1
39. 22v+ 9w-10v
40. 2(R+ S)+ 4R-1
B-26
102
Unit In Non-Negative Numbers of Arithmetic Test B
DIRECTIONS: Do not write on this test booklet. Place all answers on theanswer sheet. Do all scratch work on the paper provided to you. Do notspend too much time on any one problem.
COMPLETION:
1. The multiplicative identity element is2. has no reciprocal.3. The additive identity element is4. If x is the multiplicative inverse of a, then (x) (a) =
5. By the transitive property of equality, if B= a+ 2 and a+ 2 = D, then
In problems 6-11, write the answers for each problem. If the group ofsymbols has no meaning, write "no meaning" on the sheet.
6.
07.
5
S. (6)(1)0
9.
10. 7. 0
511.
0
Simplify the following expressions.
12. 9(4a )
113.
3(15xy)
14. (7x)(9y)
In problems 15 -17, tell whether the statement is TRUE or FALSE.15. {0, 1} is closed under the operation of multiplication.16. {0, 1} is closed under the operation of addition.17. The set of odd numbers is closed under the operation of addition.
B-27
103
In problems 13-22, write the letter of the property which is illustrated bythe example below.
A. Reflexive Property of EqualityB. Symmetric Property of EqualityC. Transitive Property of EqualityD. None of these
13. If 4-1 = 3 and 3 = 2+1, then 4-1 = 2+1.19. If 7 = 5+2, then 5+ 2 = 720. 6(3. 5) = (6. 3)5
21. If 6+ 2, = 3, then 8 = 6 +2
22. 7 =
In problems 23-27, write the letter of the property which is illustrated bythe example below.
A. Commutative Property of Addition
B. Associative Property of AdditionC. Commutative Property of MultiplicationD. Associative Property of MultiplicationE. Distributive Property of Multiplication over Addition
23. 7+2 = 2+7
24. 6 +(3 +5) = (6+3)+5
25. 9+ '2. 3) = (2. 3)+ 9
26. 3(6+ 1) = 3' 6 + 3' 1
27. 4(3 n) = (4. 3)nIn problems 28-32, write the letter of the property which is illustrated bythe example below.
A. Additive Property of ZeroB. Multiplicative Property of ZeroC. Multiplicative Property of OneD. None of these
B-28
104
23. 17.1 = 17
29. 0. 16 = 16
30. 15+1 = 16
31. (3. 2)+0 = 3. 2
32. 4.0=
Write the reciprocal of:
33.37
34. 9
35. 1
36. Which term is similar to 5b? Write the letter of the correct answer
on the answer sheet.
A. 5ab
B. 5a
C. 5
D. 4b
E. None of these
In problems 37-40, combine by adding or subtracting similar terms.
37. 9b+6b
38. 4q+ 7q+ 12
39. 36a+7b-20a
40. 6(a +b)+ 3b- 4
B.;29
105
0 Unit III Non-Negative Numbers of Arithmetic Test C
DIRECTIONS: Do not write on this test booklet. Place all answers on theanswer sheet provided to you. Do all scrap work on the paper provided toyou for this purpose. Do not spend too much time on any one problem.COMPLETION:
1. The additive identity element is
2. The multiplicative identity element is3. By the transitive property of equality, if a= b+ 3 and b+ 3= Q, then
4. has no reciprocal.5. If a is the multiplicative inverse of b, then ab =
Write the answers for each problem in arithmetic. If the group of symbolshas no meaning, write "no meaning" on the sheet.6. (1)(20) =
7. 49. 0 =
718.
0
9.
10.
11.
3
1
00
0
9
Simplify the following expressions.
12. 3(4w)
13.1
3(24RS)
14. (7x)(9y)
15. TRUE or FALSE:multiplication.
The set {0, 1} is closed under the operation of
16. TRUE or FALSE:addition.
The set {0, 1} is closed under the operation of
17. TRUE or FALSE: The set of even numbers is closed under theoperation of multiplication.
B-30
10
In problems 18-22, write the letter of the property which is illustrated bythe example below.
A. Reflexive Property of EqualityB. Symmetric Property of EqualityC. Transitive Property of EqualityD. None of these
18. If 7 = 3-1 then 8-1 = 719. 15 = 15'
20. If 6-2 = 4 and 4 = 3+1, then 6-2 = 3+121. 5(3. 2) = (5. 3)2
22. If 3+ 2 = 5 then 5 = 3+2
In problems 23-27, write the letter of the property which is illustrated bythe example below.
A. Commutative Property of AdditionB. Commutative Property of MultiplicationC. Associative Property of AdditionD. Associative Property of MultiplicationE. Distributive Property of Multiplication over Addition
23. 7+9 = 9+724. 3(2n) = (3. 2)n for all numbers n.25. 5(3+2) = 5. 3 + 5. 226. 3+ (2+7) = (2+7)+3
27. 5+ (4+ 1) = (5+ 4)+ 1
In problems 28-32, write the letter of the property which is illustrated bythe example below.
A. Additive Property of ZeroB. Multiplicative Property of ZeroC. Multiplicative Property of OneD. None of these
23. 0. 14 = 14
29. 12 +1 = 13.
30. 5.0= 031. (9. 3)+0 = 9. 3
32. 16.1 = 16107
B-31
Write the reciprocal of:33. 5
7
34. 6
35. 1
36. Which is similar to 7b:A. 7
B. 4c
C. 6bc
D. 4b
E. None of these
Combine by adding or similar terms.37. 3a + 7a
33. 10w-6w+ 12
39. 23q+ 3r-5r40. 3(r+ s )+ 4r -1
B-32
108
Unit III Non-Negative Numbers of Arithmetic Test D
DIRECTIONS: Do not write on this test booklet. Place all answers on theanswer sheet. Do all scratch work on the paper provided to you. Do notspend too much time on any one problem.
COMPLETION:
1. By the transitive property of equality, if N= a-3 and a -3= B, then
2. The additive identity element is3. The multiplicative identity element is4. If x is the multiplicative inverse of y, then (x)(y) =5, has no reciprocal.
In problems 6-11, write the answers for each problem. If the group ofsymbols has no meaning, write "no meaning" on the sheet.6. 15. 1
7. 51
3. 90
9. 9. 0
10.00
11.9
Simplify the following expressions.12. 5(3a)
113.
5(20xy)
14. (3x) (5y)
In problems 15-17, tell whether the statement is TRUE or FALSE.15. The set of odd numbers is closed under the operation of multiplication.16. { 0, /} is closed under the operation of addition.17. {0, 1} is closed under the operation of multiplication.
B-33
109
In problems 18-22, write the letter of the property which is illustrated bythe example below.
A. Reflexive Property of Equality13. Symmetric Property of EqualityC. Transitive Property of EqualityD. None of these
13. 5(3. 4) = (5. 3)4
19. 7 =
20. If 7+3 = 10, then 10 = 7+321. If 5+2 = 7 and 7 = 6+1, then 5+2 = 6+122. 9+ 3 = 9 +3
In problems 23-27, write the letter of the property which is illustrated bythe example below.
A. Commutative Property of AdditionB. Associative Property of AdditionC. Commutative Property of MultiplicationD. Associative Property of MultiplicationE. Distributive Property of Multiplication over Addition
23. 5+(3+2) = (5+3)+224. 3+3 = 3 +9
25. 6. (3. 5) = (6. 3)5
26. 4(6 +2) = 4. 6 + 4. 2
27. 3. 5 = 5. 3
In problems 28-32, write the letter of the property which is illustrated bythe example below.
A. Additive Property of ZeroB. Multiplicative Property of ZeroC. Multiplicative Property of OneD. None of these
23. 7. 0 = 029. 3. 0 = 3
30. 17.1 = 1731. 13-3 = 15
32. (5. 6)+ 0 = 5.6 110
B- 3 4
Write the reciprocal of:33. 1
34. 6
35.7
3
36. Which term is similar to 4c? Write the letter of the correct answeron the answer sheet.A. 4b
B. 4
C. 6c
D. 4ac
E. None of these
In problems 37-40, combine by adding or subtracting similar terms.37. 8a + 9a33. 6a + 4a-539. 12a - 6b + 4a40. 6(x+y) - 3y +4
13-35
11
UNIT III Non-Negative Numbers of Arithmetic A B C D
NAME SECTION
TEACHER DATE
SCORE PERICD
1. 23.
2. 24.
3. 25.
4. 26.
5. 27.
6. 28.
7. 29.
3. 30.
9. 31.
10. 32.
11. 33.
12. 34.
13. 35.
14. 36.
15. 37.
16. 38.
17. 39.
13. 40.
19.
20.
21.
22.
B-36
.112
Unit IV The Negative Numbers Part ITest A
DIRECTIONS: Do not write on this test booklet. Work carefully, but donot spend too much time on any one problem. Place the answer in theappropriate space of the answer sheet provided to you.
State which number in each pair is the greater for numbers 1 to 5.1. 5, -92. -4, -3
3. -220, 03
4. 4'7
1 15. 4' -46. TRUE or FALSE: All numbers are positive or negative.
Refer to the following number line for problems 7 to 9 .
GFED OI A B C
-4 -3 -2 -1 0 1 2 3 4
7. Which point would be associated with a loss of three dollars?
3. Which point would be associated with a gain of two yards?
9. Which point would be associated with a temperature of one degreebelow zero?
10. COMPLETION: To subtract b from a, we theadditive inverse of b to a.
11. TRUE or FALSE: Subtraction is a commutative operation.12. COMPLETION: To divide a by b, we multiply a by the of b.
13. COMPLETION: To say that n<0 for some number n is the same as sayingthat n is a (positive, negative) number.
Write the additive inverse of each number in problems 14 through 17.
14. 9
15. -4
16.
17.. 0
1
5
B-37
1
COMPLETION: When two numbers that are additive inverses areadded, the sum is always
19. COMPLETION: The absolute value of +20 is20. 1-41
21. I 0
22. TRUE or FALSE: 1-31 = 1 3
In problems 23 to 39, perform the indicated operation and write the answerto each on the answer sheet.
23. (+ 15) + (+ 17) =
24. (+8) + (-4) =
25. (+ 16) + (-23) =
26. (-17) + (+9) =
27. (-54) + (-19) =
23. (-20) + (+29) =
29. (+9) (+4) =
30. (-4) (-7) =31. (-17) (+3) =
32. (+16)4. (+4) =
33. (-32)4- (-16) =
34. (-100):: (+25) =
35. (+25):- (-5) =36. (+23) + (-17) + (-30) + (+6)37. (+ 13) - (+ 10)
38. (-10) - (+10)39. (+31) - (-41)
B-38
114
Unit IV The Negative Numbers Part ITest B
DIRECTION: Do not write on the test booklet. Work carefully, but do notspend too much time on any one problem. Place the answer in theappropriate space on the sheet provided to you.
State which number in each pair is the greater for numbers 1 to 5.1. 4, -72. -7, -63. -167, 0
54.
6 3
2
1 15.
3 -3
6. TRUE or FALSE: All numbers are positive or negative.
Refer to the following number line for problems 7-9.
HG FED 0 T. A BC$ 4 I I I
1I
-5 -4 -3 -2 -1 0 1 2 3 4
7. Which point would be associated with a gain of three dollars?3. Which point would be associated with a loss of two yards?9. Which point would be associated with a temperature of 4 degrees
above zero?10. TRUE or FALSE: To subtract b from a, we subtract the additive
inverse of b from a.11. TRUE or FALSE: Subtraction is a commutative operation.12. COMPLETION: To divide b by a, we multiply b by the
of a.
13. COMPLETION: To say that n>0 for some number n is the same assaying that n is a (positive, negative) number.
Write the additive inverse of each number in problems 14 through 19.
14. 7
15.
B-39
115
16.2
-3
17. 0
13. TRUE or FALSE: When two numbers that are additive inverses are1.dd.e2 the sum is always zero.
19. COIviPLETICN: The absolute value of +16 is20. I-31 =21, 0 I =
22. TRUE or FALSE: 5 1= I-51
In problems 23 to 39,, perform the indicated operation and write the answeron the answer sheet.
23. (+ 14) + (I- 19)
24. (+7) + (-3)25. (-16) + (+10)26. (+ 12) + (-13)
27. (-63) + (-17)28. (-4) + (+17)
29. (+3) (+3)30. (-5) (+6)31. (-17)(+4)
3Z. (+13)4- (-V 2)
33. (-20) 4- (-5)
34. (-250)4 (+125)35. (+36)-:- (-6)
36. (+6) + (-7) + (-9) + (+4)37. (+21) - (+4)38. (-6) - (+6)39. (17) - (-15)
B-40
11 6
Unit IV The Negative Numbers Part ITest C
DIRECTION: Do not write on the test booklet. Work carefully, but do notspend too much time on any one problem. Place the answer in the appropriatespace on the sheet provided to you.
State which number in each pair is the greater for numbers 1 to 5.1. 3, -7
2. -6, -23. -100, 0
1 34. 4' 3
5.1 1
3' 3
6. TRUE or FALSE: All numbers are positive or negative.Refer to the following number line for problems 7 to 9.
I FIG F E 0 J A B C D
-5 -4 -3 -2 -1 0 1 2 3 4 5
7. Which point would be associated with a loss of five dollars?3. Which point would be associated with a gain of one yard?9. Which point would be associated with a temperature of two degrees
below zero?10. COMPLETION: To subtract a from b, we the additive
inverse of a to b.11. TRUE or FALSE: Subtraction is a commutative operation.12. COMPLETION: To divide a by b, we multiply a by the
of b.
13. COMPLETION: To say that x<0 for some number x is the same as sayIngthat x is (positive, negative) number.
Write the additive inverse of each number in problems 14 through 17.14. 3
15. -7
16.
17. 0
1
3
B-41
1 /
la. COMPLETION: When two numbers that are additive inverses areadded, the sum is always
19. COMPLETION: The absolute value of +31 is20. I -91 =
21. 0 =
22. TRUE or FALSE: I -111 = 111
In problems 23 to 35, perform the indicated operation and write the answerto each on the answer sheet.
23.
24.
(+ 12) + (+ 19) =
(+ 10) + (-3) =
25. (+18) + (-21) =
26. (-13) + (+9) =
27. (-72) + (-17) =23. (-30) + (+39) =
29. (+15) (+3) =30. (-3) (-7) =
31. (-17) (+2) =
32. (+15):- (+3)=
33. (-30) 4- (-15) =
34. (-125) (+25) =
35. :+35)-: (-7) =36. (+23) + (-17) + (-20) + (+5 ) =
37. (+ 18) - (+6) =
33. (-10) - (+9) =39. (+50) - (-40) =
B-42.
Unit IV The Negative Numbers Part ITest D
DIRECTION: Do not write on the test booklet. Work carefully, but do notspend too much time on any one problem. Place the answer in the appropriatespace on the sheet provided to you.
State which number in each pair is the greater for numbers 1 to 5.1. 6, -32. -2, -43. -160, 0
4.4.5 3
2
5.1 1
5' 5
6. TRUE or FALSE: All numbers are positive or negative.Refer to the following number line for problems 7 to 9.
1,>
7. Which point would be associated with a loss of four. dollars?9. Which point would be associated with a gain of two yards?
9. Which point would be associated with a temperature of 2 degreesbelow zero?
10. TRUE or FALSE: Subtraction is commutative.11. COMPLETION. To say N<0 for some number N is the same as saying
that N is a (positive, negative) number.
12. COMPLETION: To divide b by a, we ltiply by the of a.
13. TRUE or FALSE: To subtract b from a, we add the additive inverse ofof b to a.
Write the ac'ditive inverse of each number in problems 14 through 17.14.
15. -2
16.5
-7
17. 0
B-43
119
18. TRUE or FALSE: When two numbers that are additive inverses areadded, the sum is always zero.
19. COMPLETION: The absolute value of +17 is20, -41=
21. I 01=
22. TRUE or FALSE: I 41 = I-4I
In problems 2.3 to 36, perform the indicated operation and write the answeron the answer sheet.
23. (+7) + (+ 16)
24. (+4) + (-2)25. (-14) + (+7)26. (+ 11) + (-13)
27. (-42) + (-16)28. (-3) + (+14)29. (+9) (+4)30. (-6) (+4)
31. (-15) (+3)
32. (+20)-: (+4)
33. (-15)4 (-5)34. (-75)+ (+25)35. (+42)4- (-6)
36. (+4) + (-3) + (+5) + (-9)37. (+6) - (+3)39. (-15) (+7)
39. (+21) - (-6)
B-44
.12
UNIT IV
NAME
TEACHER
SCORE
1.
2.
3.
4.
5.
6.
7.
B.
9.
10.
11.
12.
13.
14.
15.
16.
17.
13.
19.
20.
21.
22.
23.
24.
25.
The Negative Numbers PART I ABC D
SECTION
DATE
PERICD
26.
27.
23.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
B-45
121
UNIT IV The Negative Numbers PART IITEST A
DIRECTICNS: Do not write on the test booklet. Place the correct answeron the sheet provided.
Write the reciprocal of each number in problems 1-4.1. 1
2. -4
3.
4.
125
5
4
5. COMPLETION: If b is the multiplicative inverse of a, then(a)(b) =
6. COMPLETION: has no multiplicative inverse.Place "positive" or "negative" in the appropriate space. (7-8)
The value of any even power of a negative number is a (7)number, while the value of any odd power of a (8)number is a negative number.
Perform the indicated operations in problems 9-11.9. (-5x) (3y) =
10. (-2a)3=
11. (-2a) 2ri
12. TRUE or FALSE: The set of negative integers -3, -2, is closedunder multiplication.
13. TRUE or FALSE: The set of negative integers {... -3, -2, -1} is closedunder addition.
14. 3x - (-2x) =
15. by + Sy - 24y =
16. ADD: 6x - 2y - 3zZx + 2y+ 4z
17. 3x - (2x-y) =18. (5a+ 2b) + (7a -3b) =
19. (6x-y) - 3 (2x+y) =
20. EVALUATE: If a = -2, b = -3, and c = -I, then 2a-3b+c =
UNIT IV The Negative Numbers PART IITEST B
DIRECTIONS: Do not write on this test booklet. Place the correct answeron the sheet provided.
Write the reciprocal of each number in probleras 1-4.
2. -8
3.43
4. 1
5. COMPLETION: If b is the multiplicative inverse of a, then(a)(b) =
6. COMPLETION: has no multiplicative inverse.
Place "even" or "odd" in the appropriate space on your answer sheet. (7-8)
Any _(21... power of a negative number is a negative,while any (8) _power of a negative number is a positivenumber.
Perform the indicated operation in problems 9-11.
9. (-35)(7y) =10. (-3a)1 =
11. (-3y)3 =
12. TRUE or FALSE: The set of negative integers {... -3, -2, -1} is closedunder multiplication.
13. TRUE or FALSE. The set of negative integers {... -3, -2, -1} is closedunder addition.
14. 4x - (-3x) =15. 7y + 9y - 23y =16. ADD: 5x-2y-4z
3x+ 2y+ 5z
17. 3x - (5x-2y) =
19. (4a+ 9b) + (2a -7b) =
19. (9x-2y) -3 (x+4y) =
20. EVALUATE: If a = -1, b = -2, and c = -3, then 2a-3b+c =
IMMEMNIMMMIND
UNIT IV The Negative Numbers PART IITEST C
DIRECTIONS: Dc not write on the test booklet. Place the correct answeron the sheet provided.
Write the reciprocal of each number in problems 1-4.
1. 3
2. -5
3.
4.
5
13
5
5. COMPLETION: If b is the multiplicative inverse of a, then (a)(b) =
6. COMPLETION: has no multiplicative inverse.Place "positive" or "negative" in the appropriate space. (7-8)
Th value of any even power of a negative numbernumber, while the value of any odd power of ais a negative number.
P(.rform the indicated operations in problems 9-11.9. (-3y)(5x)
10. (-2b)3
11. (-2c)2
12. TRUE or FALSE:under multiplicati
13. TRUE or FALSE:under addition.
A4. 5y, - (-zy)
15. 3x+ 8x - 19x=
The set of negativeon.
The set of negative
is a (7)(8) number
"integers {... -3, -2, -1} is closed
integers {... -3, -2, -1} is closed
16. ADD: 7x - 2y + 3z2x+ 2y - 4z
17. 3x - (2x+y) =
13. (5c4 3b) + (8c-5b) =
19. (6x-y) - 2 (3x-y) =
20. EVALUATE: If a= -2, b= -3, c= -1, then 3x-2b+c =
UNIT IV The Negative Numbers PART IITEST D
DIRECTICNS: Do not write on this test booklet. Place the correct answeron the sheet provided.
Write the reciprocal of each number in problems 1-4.
1.2
5
2. -6
43.
7
4. 5
5. CCMPLETIC;N: has no reciprocal.6. COMPLETICN: If b is the multiplicative inverse of a, then (a)(b) =
Place "positive" or "negative" in the appropriate space. (7-8)
The value of any even power of a negative number is (7)number, while the value of any odd power of a (9)number is a negative number.
Perform the indicated operations in problems 9-11.
9. (-2Y)(3x) =
10. (-4a) 2=
11. (-3a) 3=
12. TRUE or FALSE: The set of negative integers -3, -2, -1} is closedunder multiplication.
13. TRUE or FALSE: The set negative integers {... -3, -2, -1} is closedunder addition.
14. 4x - (-3x) =
15. 3y 4y - 9y =16. ADD: 9y. - 3y + 4z
2x 4z_
17. 9x - (3x-Zy) =
18. (4a+ 2b) + (6a -3b) =
19. (2x-y) - 2 (3x+y)
20. EVALUATE: If a= -1, b= -2, and c= -3, then 2a-3b+c =
125B-49
UNIT IV
NAME
TEACHER
SCORE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
H.
12.
13.
14.
15.
16.
17_
18.
19.
20.
The Negative Numbers
B-50
1 2 (-)
P A R T I I A BCD
SECTION
DATE
PERIOD
UNIT V Open Sentences, Equations, and Inequalities TEST /-1.
DIRECTIONS: Do not write on this test booklet. Place all answers andsolutions on the answer sheets provided to you. Do all work on the scratchpaper provided to you. Do not spend too much time on any single problem.Unless otherwise stated, the replacement set of all equations is the set ofnumbers of arithmetic.
Complete the following paragraph by filling in the blanks with words fromthe following list: Write the letter of the correct answer on the answer sheet.
A. OPEN SENTENCE B. INEQUALITY C. SCLUTIC N SET
D. REPLACEMENT SET E. RIGHT MEMBER F: EQUATICN
G. LEFT MEMBER H. SOLUTIGN
Consider the set { 1, 2, 3, 4, 5} and the statement Zx + 3 = 4x. Since2x + 3 = 4x contains a variable and, hence, has no truth or falsity, itis called a(n) (1) . When x is replaced by the name ofa number, the statement 2x + 3 = 4x becomes then either a true orfalse 2 . If the statement 2x + 3 = 4x becomestrue when x is replaced with the name of a number, then the replacementnumber is called a(n) (3) of the statement. If xcan be replaced only with members of the set { 1, 2, 3, 4, 5}, then thisset is called the (4) of x.
5. TRUE or FALSE: 3 is a. solution of the open sentence
x2 - 5x + 6,= 0
Solve each of the following open sentences. The replacement set is the setof numbers of arithmetic. Place the solutions in the answer sheet.6. a + 2 = 57. d + 5 = -73. -10= x- 39. y+ = -4
10. 5 - m= -1011. 3x 9
12. 5d 7: 17
13. 6x = -2014. -15z = 52
B -51
197.
15. -36 = -7a16.
3 x = 7
17. = -3
18. 1. 4x = 6
19. Ga - 13 = 30
20. 5b + 9 - 3b = 2021. 15 - 4a + 3a= 1722. 5d - 7 = 3d23. 3(5-z) =
24. -6 (6+4x) = 1925. 5(3+2x) - 4x = 7x -
26. If A = {5, 4, 3, 2, 1, 0} is the replacement set of x in he open sentence
x - 3 = 2
then the solution ` set of the open sentence is
27. Graph the solution set of5x> 10
on the number line provided on the answer sheet. The replacementset for x is the set
{0, 1, 2, 3, 4,5,6,7, 8, 9}
Solve each of the following inequalities. The replacement set in each caseis the set of real numbers.
28. -6b> 13
29. d + 4 > 9
30. 5(2a-1) < 4
a31.
2< 6
332. - 4c < -7
33. Graph the solution set of x < 3 on the number line provided on youranswer sheet.
34. John scored twice as many points as Jim. If Jim scored a 45, what wasJohn's score?
B-52
19(.3
UNIT V .pen Sentences, Equations and Inequalities TEST B
Complete the following paragraph by filling in the blanks with words fromthe following list: Write the letter of the correct answer on the answer sheet.
ti
A. open sentence E. solution setB. equation F. inequality
C. left member G. replacement setD. right member H. solution
Consider the set { 2, 3, 5, 6} and the statement 3x +4= 4x. Since 3x +4= 4xcontains a variable and hence has no truth or falsity, it is called a (n) (1)When x is replaced by the name of a number, the statement 3x +4= 4x becomeseither a true or false (2) . If the statement 3x +4= 4x becomestrue when x is replaced with the name of a number, then the replacementnumber is called a (n) (3) of the statement. If x can be replacedonly with members of the set { 2, 3, 5, 6 }, then this set is called the (4)
5. TRUE or FALSE: 2 is a solution of the open sentence x2 -5x +6= 0.
Solve each of the following open sentences. The replacement set is the setof numbers of arithmetic. Place the solutions on the answer sheet.6. a+ 4= 5
7. d+5= -63. -10 = x+ 3
19. y+ -2- 4
10. 4-m = -1011. 3x= 12
12. 5d = 11
13. 6x = -4014. -15z = 53
15. -37 = 9a3
16.4---x = -15
17. 4= -4
14. 1. 6x = 6
B-53
129
19. 3a-13 = 30
20. 6b+1-3b = 20
21. 15-5a+4a = 17
22. 6d-7 = 4d
23. 2(5-z) = 6
24. -5(6+4z) = 19
25. 6(3+ 2x)-4x = 8x-9
26. If A = {5, 4, 3, 2, 1, 0} is the replacement set of x in the open sentence3x-2 = 4x, then the solution set of the open sentences is
27. Graph the solution set of 4x >8 on the number line provided on theanswer sheet. The replacement set for x is the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.
Solve each of the following inequalities. The replacement set in each caseis the set of real numbers.
23. -6b> 9
29. d-4>9
30. 5(2a+ 1)< 4
31. <63
332. --5 c> -9
33. Graph the solution set of w>-4 on the number line provided.
34. Bob earned ::,.4 less than Mark. If Mark earned how much did Bob earn?
B-54
133
UNIT V Open Sentences, Equations, and Inequalities TEST C
DIRECTICNS: Do not write on test booklet. Place all answers and solutionson the answer sheets provided to yuu. Do not spend too much time on anysingle problem. Unless otherwise stated, the replacement set of all equationsis the set of numbers of arithmetic.
Write the letter of correct answers on the answer sheet.A. open sentence E. right memberB. inequality F. equation
C. solution set G, left memberD. replacement set H. solution
Consider the set 1. 2. 3. 4. 5} and the statement 3x+ 2 = 4x. Since 3x+ 2 = 4xcontains a variable and, hence, has no truth or falsity, it is called a(n) (1) . When x is replaced by the name of a number, thestatement 3x+ 2 = 4x becomes either a true or false (2)If the statement 3x+ 2 = 4x becomes true when x is replaced with the namea number, then the replacement number is called a (n)of the statement . If x can he replaced only with members{ 1, 2, 3, 4, 5} , then this set is called the (4)
5. TRUE or FALSE: 3 is a solution of the open sentence
- 4x + 5 = 0
(3)of theof x.
Solve each of the following open sentences. The replacement set is the setof numbers of arithmetic. Place the solutions on the answer sheet.
6. x + 3 = 57. y + 5 = -33. -10 = x - 2
19. y+ -2- = -9
10. 5 - m = -1511. 3x = 12
12. 4x = 19
13. 5x= -1314. -11R = 44
15. -35 = -6a
16.2x = 93
B-55
131
17.7
= -5
18. 1. 4x = 8
19. Za - 12= 4020. 5a + 7 - 2a = 2021. 12 - 4a + 3a= 1522. 5y 6 = 3y
23. 3(2-w) =
24. -4(6+3x) = 13
25. 5(2+ 3x)-5x = 7x-3
26. If A = {5, 43 3, 2, 1, 0} is the replacement set of x in the open sentencex - 5 = 4
then the solution set of the open sentence is27. Graph the solution set of
3x >12
on the number line provided on the answer sheet. The replacement setfor x is the set
{0, 1, 2,3, 4,5, 6, 7, 8, 9)
Solve each of the following inequalities. The replacement set in each case isthe set of real numbers.
28. -5a> 12
29. b+ 3 > 930. 5(2x- 1)< 6
31.3
<6
32. --2R< -73
33. Graph the solution set of x <5 on the number line provided on youranswer sheet.
34. Cne number is 15 more than another number. The sum of the number is65. Find the larger number.
B -56
132
UNIT V (*pen Sentences, Equations and Incqualitiev TEST D
Complete the following paragraph by filling in the blanks with words fromthe following list. Write the letter of the correct answer on the answer sheet.
solution set E. left memberB. open sentence F. right memberC. inequality G. replacement setD. equation H. solution
Consider the set { 1, 2, 3, 4, 6} and the statement 3x-2 = x. Since 3x-2; = xcontains a variable and, hence, has no truth or falsity, it is called a(n) (1) . When x is replaced by the name of a number, thestatement 3x - 2 = x becomes either a true or false (a)If the statement 3x - 2 = x becomes true when x is replaced with thename of a number, then the replacement number is called a (n) (3)of the statement. If x can be replaced only with members of the set{1, 2, 3, 4, 6 }, then this set is called the (4)
5. TRUE or FALSE: 3 is a solution of the open sentence(x+ 3)(x-2) = 3
Solve each of the following open sentences. The replacement set is the setof numbers of arithmetic. Place the solutions on the answer sheet.6. x + 7 = 97. y+ = -3S. -5 = x + 9
19. y + -3- = 6
10. 5 - m = 1611. 4x = 16
12. 7d= 1113. 8y = 34
14. -15a = 5615. -61 = 5a
716. -8-y = -21
17. m = -23
18. 1.5x= 719. 2a - 12 = 27
B-57
133
20, + 5 - 3b = 1621. 12 - 6a + 5a = 1522. 8d - 5 = 3d23. 4(z+6) = 33
24. -4(6+ 2z) = 17
25. 5(3 +2x) -4x = 8x-9
26. If A = {3, 2, 1, 0} is the replacement set of x in the open sentence 2x-1= 5x,then the solution set of the open sentence is
27. Graph the solution set of 6x>12 on the number line provided on the answersheet. The replacement set for x is the set {0, 1, 2, 3, 4, 5, 6).
Solve each of the following inequalities. The replacement set in each caseis the set of real numbers.
23. -3y> 6
29. d-3>9
30. 4(2a+ 1) < 3
31.a<6
3>32. --4 c -12
33. Graph the solution set of x< -2 on the number line provided.
34. Mary scored 7 points better than Judy. If Mary scored a 91, what wasJudy's score?
B-58
134
UNIT V
NAME
TEACHER
SCORE
Open 3entenceE, Equations and Inequalities
SEC TIC. N
D.etTE
PERIOD
ABCD
1. 26.
2.
3.
4.
5.
6.
7.
8. 279. -1 0 1 2 3 4 5 6 7 3 9 10
10.
11. 23.
12. 29.
13. 30.
14. 31.
15. 32.
16. 33.
17. -4 -3 -2 -1 0 1 2 3 4
13.
19.
20.
21. 34.
22.
23.
24.
25.
13-59
1?
UNIT VI Polynomials TEST A
DIRECTIONS: Do not write on this test paper. Do all scratch work onthe paper provided to you for this purpose. Place all your answers onthe answer sheet. Do not spend too much time on any single problem.
Which expressions in the following list are not polynomials? Place theletter preceding the correct answer or answers on the answer sheet.
1. A. x3 - ?x 2 + 6x - 51B.3x5 - 2x2 + 9
C. 5x
D. 4
E. (x-2) (x+ 3)
F. 7x2 - 5x + 3 - -2-x
G. x2 - 5x + 2x - 3
H. 3x2y - 2xy2 + 6y - 3
2. Which expression in the following list is a trinomial? Place theletter or letters preceding the correct answer or answers on theanswer sheet.
A. 5x C. x3 - 3x + 5
B. ?x2 - 2 D. ?x4 - 3x2 + 6x - 2
3. What is the degree of 5x4 - 2x 2 + 6x - 3?
4. What is the degree of 3x 2y- 6xy2 - 5x + Zy - 3?
For problems 5-31, write the letter of the correct answer on the answer sheet.
5. Arrange the following polynomial in descending order.4x3-3 + 4x2 5x
A. -3 -5x + 4x2 + 4x3
B. 4x3 + 4x 2 - 5x - 3C. 4x3 - 3 + 4x2 - 5x
6. -ADD: (5x2-6x+ 9) + (?x-4)
A. 5x2 + x + 5B. 6x3+ 5
C. 5x2 - 13x - 23D. None of the above
B-60
1'46
7. ADD: 8x 3 - 2x2 + 5x - 3
3x3 + 2x + 7x + 9
A. 5x3 - 2x - 12
B. 5x3 + 12 + 6
C. 11x3
- 4x2 + 12x + 6
D. 11x3 + 12x + 6
3. SUBTRACT: (4x2-3x-2) - (2x2-7x+ 3)
A. 2x2 - 10x +1
B. 2x2 + 4x - 5
C. 6x2 - 10x + 1
D. 6x 2 + 4x - 5
9. SUBTRACT: (2x3 - x -7) - (2x
2 -2x+3)
A. -4x2 - 2x - 10B. -4x2 + 2x - 4C. 2x
3 - 2x2 - 2x - 4D. 2x 3 - 6x2 + 2x - 10
10. SUBTRACT: 7x2y - 3xy2
3x2y 3xy2
A. 4x2y,B. 2y - 6xy2
C. 10x2y 6xy2
D. None of the above
/1. What is the additive inverse of 3x2 - 2x + 4 ?
A. -3x2 + 2x +4
B. -3x2 + ;2x - 4
C. 3x2 + 2x 4
D. 3x2 - 2x +4
B-61
1 '47
12. Which of the following "laws" are incorrect?
A. am an = am+n, m and n are positive integersB. (am)n = amn, m and n are positive integersC. (ab) = abm, m is a positive integerD. None of the above
13. SIMPLIFY: x3 x2 =
A.
B. x5
C. x9
D. None of the above
14. (a5)2 =
__. a7
3. al0C. a 25
15. b15
b3
16.
A. b5
B. b18
C. b1Z
d9
d3
A. d6
B. d12
C. d3
17. (xy)5=
5A. xy
B. x5y
C. x5 y5
D. None of the above
B
18. (5x202
A. 25x4y
B. 5x4 y2
C. 5x4y
D. 25x4 y2
19. (3a 2)(2a 9)
A. 5a11
B. 5a19
C. 6a11
D. 6a18
20. (-5g 2)3=
A. -125g 5
B. 125g5
C. -125g 6
D. -125g 3
21. (4x2 yz3)(-2xy3z2)
A. 9x2y3z
6
B. 8x3 y4
z5
C. -8x2y 3z
6
D. -8x3 y4z
5
22. (33t2v) 2 (-3s 2tv3)2
A. 81s6t61,6
E. -81s 6t6v6
C. 81s8t8v8
D. None of the above
23. MULTIPLY: 3x2 (5-2x+ 7x2)
A. 15x2 6x + 21x 4
B. 15x'- - 6x 3 + 21x 4
C. 5x2 -6x3 + 21x4
B-63
139
24. MULTIPLY: 5y2-3y + 23y - 4
A. 15y3
- 11y2 + 1 Ry - 8
B. 15y3 + 29y2 + 18y - 8
C. 15y2 - 29y2 + I8y - 8
25. MULTIPLY: (4x-3)(5x+1)
A. 20x 2 - 1 lx - 3B. 20x2 + 1 lx - 3C. 20x 2 - 19x - 3D. 20x 2 + 19x - 3
26. MULTIPLY: (x-4)2
A. x2- 16
B. x2 + 16
C. x2+ 3x+ 16
D. x2 - 3x + 16
27. MULTIPLY: (2x+ 1)
2A. 4x + 1B. Lx
2 + 1
C. 4x 2 + 4x + 1D. 2x2 f 4x + I
2
23. DIVIDE: 5x / 10x4+ 5x3-5x2+ 25x
A. 2x3
+ x2 - x + 5B. 2x4 + x3 - x2 + 5xC. 2x
3+ x2 + 5
D. 2x4
+ x3 + 5x
B-64
143
29. DIVIDE: x-7 x2-9x+
14
A. x+16+ x-7
B. x-16+ x26-7
C. x +2
D. x - 2
30. DIVIDE:
A.
B.
C.
D.
2x-5 .I 6x
3x 2 + 8x +11 +
3x2 + 3x + 11
2
5-'2.-+ x -19x-33
2x22-5
3x - 7x + 9 + 2x-5
None of the above
2 I 531. DIVIDE: 6x -3 112x -12x` 3x
A. 2x3-3x
B. 2x3-3x +
C. 2x3 - x +
D. 2x3-x
-6x
6x2-3
-6x
6x2-3
32. COMPLETICN: a° =
33. COMPLETION: al
, a iL 0
34. The sum of three times a number and twice the number is decreased by15, the result is 165. Determine the number.
B -65
141
UNIT VI Polynomials TEST B
Which expressions in the following list are not polynomials? Place theletter preceding the correct answer or answers on the answer sheet.
1. A. 5x4 - 7x3 + 32x2 -5x + 2 E. (x-1) (x+3)
1 6 4B. x - 3x 2 + 9 - F. 8x2 - 12x + 3 -X3
C. 5x - 3 G.
D.
x2 - 5x + 2x - 3
H. 3x2y 2xy2 + 6y - 3
y
2. Which expression in the following list is a trinomial.? Place the letterpreceding the correct answer or answers on your answer sheet,
A. 5x C. x3 - 3x + 5
B. 7x2 - 2 1D. 7y4 - 3y 2 + 6y - 2
3. What is the degree of 5x5 - 2x2 + 6x + 3 ?
4. What is the degree of 3x2y3 - 6xy2 - 5x + 2y - 3 ?
Fcr problems 5 - 31, write the letter of the correct answer on the answersheet.
5. Arrange the following polynomial in descending order4x 3 - 3 + 4x2 + 5x4
A. -3 + 4x2 + 4x3 + 5x4
B. 4x3 - 3 + 4x2 + 5x4
C. 5x4 + 4x3 + 4x2 - 3
6. ADD: (3x2 - 5x +11) + (8x-4)A. 6x 3 + 7
B. 3x 2 + 3x +7
C. 3x2 - 3x -D. None of the above
B-66
7. ADD: 3x3
- Zxz + 15x + 3
4x3
+ 2x2
+ 7x+ 9
A. 12x3 + 4x2 + 22x + 12
B. 12x3 - 4x 2 + 22x + 12
12x3 + 22x + 12C.
3. SUBTRACT: (7x2-6x-2) - (2x2 -3x+4)
A.
B.
C.
D.
5x 2 - 14x + 25x
2 + 2x - 65x 2 - 14x - 25x2+ 2x + 6
9. SUBTRACT: (2x3 -4x - - (-2x 2+2x-3)
A. 2x3 - 2x 2 - 2x 4
B. 2x3 - 6x2 + 2x - 10C. 2x
3 - 2x 2 + 2x - 10D. Zx
3- 6x2 + 2x + 10
10. SUBTRACT: 8x2y 3xy 2
7x2y - 5xy2
A. 15x2y - 3xy2
B. x2y - 8xy2
C. x2y + 2xy2
D. None of the above
11. What is the additive inverse of 3x2 + 2x-3?A. -3x2 + 2x-3 C. 3x2 - 2x + 3
13. -3x2 - 2x + 3 D. -3x2 - 2x - 3
B -67
143
12. Which of the following "laws" are incorrect?
A. am. an = am+n, m and n are positive integers.B. (am)n
= an-1n , m and n are positive integers.C. (ab)m = am
bm m is a positive integer.
D. None of the above.
13. SIMPLIFY: x5 x2 =
D. None of the above
14. (a5)3
=
A. a8
B. al25C. al5
15. b25 .
b5
=
A. b 20
B. b5
C. b30
d9
16.d
6
A. d3
B. d15
C. d 3/2
17. (xy)4
A. xy4
B. x4y
4
C. x4y
D. None of the above
B-68
14,1
18. (3x 2y) 2
=
A. 3x4y
B. 9x4y2
C. 9x4y
19. (3a2)
(4a7)
=
A. 7a 9
B. 7a14
C. 12a'14
D. 12a 9
20. (-5g 2)2
A. 25g4
B. (-5)2g 4
C. None of the above
Di' Both A and B
21. (4x2yz3) (-2xy3z2) =
A. -8x2y 3z
6
B. -3x3y4z 5
C. -8x5y4z
5
22. (3st2v) 2 (-2s 2tv3)2=
A. 36s 6t6v
8
B. -36s 6t6v8
C. 36s6t6
v6
D. -36s 6 t6v 6
23. MULTIPLY: 3x2(3+3x-5x 2)
A. 9x2 + 9x3 + 15x4
B. 9x2 + 3x3- 15x2
C. 9x2 + 9x3 - 15x4
B-69
145
24. MULTIPLY: 5y2-3y+
2
3y-5
A. 15y3 + 16y 2+ 21y - 10
B. 15y3
- 34y2 + 21y - IO
C. 15y3 - 16y2
+ 21y - 10
25. MULTIPLY: (4x-3)(6x+ 1)
A. 24x - 22x + 4
B. 24x2 - 22x - 3
C. 24x2 -24x - 3
D. 24x2_ 14x - 3
26. MULTIPLY: (x-3)
A. x2 + 9B. x2 - 9C. x2 + 6x + 9D. x2 - 6x + 9
2
27. MULTIPLY: (2x-3)2
A. 4x2 - 6x + 9B. 4x 2 - 12x + 9
C. 4x 2 + 9
D. 4x2 - 9
28. DIVIDE: 5x 125x4+ I5x 3 -15x2+ 25x
A. 5x3 + 3x - 5
B. 5x3 - 3x + 5 + 5x
C. 5x3 + 3x2 - 3x + 5
D. 5x4 + 3x 3- 3x2 + 5x
tr.B-70
141E3
29. DIVIDE: x-7 ' x2
-10x+ 21
A. x-3
B. x+ 3
C. x-2+x2-7
D. Can't be done
30. DIVIDE: 2x-5 i2x3- 11x2+ 17x-5
A. x2 + 3x + 1
B. x2 - 3x + 16 + 2x75-5
C. x2-3x + 1
D. None of the above
31. DIVIDE: 6x2-3 /12x5-12x3+3x
A. 2x3-x
B. 2x3 - 3x
-C. 2x
3 - x + x6
6x2-3
6xD. 2x3 - +
6x -3
32. COMPLETION: a 1=
33. COMPLETION: a0 =
34. Twenty-one more than six times a number is 177. Determine the number.
UNIT VI Polynomial TEST C
DIRECTIONS: Do not write on this test paper. Do all scratch work on thepaper provided to you for this purpose. Place all your answers on the.answer sheet. Do not spend too much time on any single problem.
1. Which expressions in the following list are not polynomials? Place theletter preceding the correct answer or answers on the ansver sheet.
A. 3x
B. 8
1 4 2 + 7C. --x - 2x2
E. (x+ 4)(x-1)
F. 5a 2b - 2ab2 + 6b - 3
G. y +5y+2y-3
D. y3 - 7y2 + 6y - 5 H. 7R2 + 3R + - R
2. Which expression in the following list is a trinomial? Place the letteror letters preceding the correct answer or answers on the answer sheet.A. y3 - y + 4 C. 5B
2 + CB. 3x D. R4 + 3R2 - R + 2
3. What is the degree of 5x4 - 3x2 + 2.c - 1?4. What is the degree of 4a 2b - 6ab2 + 2a - 3b + 1 ?Write the letter of the correct answer on the answer sheet.5. Arrange the following polynomial in descending order:
6A3 + 1+ 3A 2 - A
A. 1 - A + 3A2 + 6A 3
B. A+ 1 + 3A 2 + 6A 3
C. 6A 3 + 3A 2 - A + 1D. None of the above
6. ADD: (4a-3b+5c) + (8a +5b-9c)A. 12a + 2b - 4c C. 12a - 8b + 14cB. 12a + 8b - 14c D. 4a + 2b - 4c
B-72
7. ADD: 3x3
-
8x3 +
2n2 + 4x - 32x
2 + 717+ 9
A.. 11x 3 - 4x2 + Ilx - 12B. 5x3 - 4x2 - 3x 12
8. SUBTRACT:
A. 3a
B. 3a + 2b
9. SUBTRACT:
C. 11x3 + llx + 6
D. -5x3 - 3x - 12
(2a+b-c) - ( a-b+c)C. a + 2b - 2cD. a + Zb +2c
(3x2-3xy2)
- Zc
(7x-? -3xy2)
A. 11x2 6xy 2
B. 4x2+ 6xy2
10. SUBTRACT: 15x2 - 3x + 92x2+ x - 3
A. 13x' - 4x + 12B. 13x2 - 2x + 6
C. 4x2 - 6xy2
D. 4x2
C. 17x2 - 2n + 6D. 17x2 - 4x + 12
11. What is the additive inverse of 5x 2 - x + 5 ?
A. -5x2 - x - 5B. 5x2 + x - 5
C.
D.
-5x2+ X - 5
5x2 + x + 5
12. Which of the following "laws" are incorrect?
A. bm bn = bm+n , in and n are positive faltegers.B. Ill )n binn m and n are positive integers,
C. (bx)m = bmx , in is a positive integer.I
Perform the indicated operations in problems 13 through 31.
132
. X x
A. x3
B. xL0
C. None of these.
B-73
14. (a3)2
A. a5 C. a6
B. a D. None of these.
15. b18 b7
A. b25 C. b126
B. 611 D. None of these.
16.R3
R9
A. R 12 C. R3
B. R6 D. None of deBe.
17. (ab)7
A. alb C. ab7
13 a7b7 D. None of these.
18. (3xy2)2
A. 6x2 y4 C. 3xy4
B. 3x2y4 D. None of these.
19. (3x2)
(4x7)
A. 7x9 C. 7x5
12x14 D. 12x9
20. (-6S2)3
A. -21655 C. 216S6
B. -216S6 D. 36S5
21. (3x2yz3) (-2xy3z2)
A. -6x3y4 5 C. 6xy4z5
B. -6xy2z D. 6x3y4z5
B-74
150
22. (2st 2v) (-3s 2tv3)2
A. -66s3 t3v4B. 36s6t
6v8
23. MULTIPLY: 3x2 (4+x-7x 2)
A. 12x2 + 3x3 + 21x 2
B. 12x2 + 3x3
- 21x4
24. MULTIPLY: 7y 2 - y + 2
23. - 9
A. 14y3 - 58y 2 - 13y - 18
B. 14y3 - 54y2 + 13y - 18
25. MULTIPLY: (2x-3) (5x+ 1)
C. -12s3t3v4
D. None of these.
C. 7x2 + 3x - 4:x2
D. None of these.
C. 14y3
- 61y2+ 13y - 18
D. None of these.
A. 10x2
- 17x + 3 C. 7x2
- 17x - 3
B. 10x2
- 17x - 3 D. 10x2
- 13x - 3
26. MULTIPLY: (y-3)2
A.
B.
y2 + 92
Y 9
27. MULTIPLY: (2x + 3)2
A. 4x2+ 9
C. y2 - 6y + 9
D. y2 + 6y + 9
C. 4x2 + 12x + 9
B. 4x2+ 6x + 9 D. 4x2 + 6
28. DIVIDE: 5M / 10M4 - 15M3 + 5M2
A. 2M3 - 3M2 + M2 C. 2M 2
+ 3M2 + M
B. 2M3- 3M2 + M D. None of these.
B-75
151
29. DIVIDE: x-7 I x2 --15x+56
A. x - 8 0C. x - 22 + 21x-7
B. x + 8 D. None of these.
30. DIVIDE: 2n-3 2n3-5n2 + 21n-14
A. n2 + 4n + 14 C.. n2- n + 12- 222n-3
B. n2 - n + 12 + 2n2 D. None of these.-23
31. DIVIDE: x2-1 x3+ 4-x-4x 2
A. x2 + 4x + 4B. x2 + 4x - 4
C. x+ 4D. x - 4
32. COMPLETION: x° = , x = 0
33. COMPLETION: x 1=
34. If the sum of three times a number and twice the number is decreasedby 15, the result is 165. Find the number.
B- 76
1 52
UNIT VI Polynomials TEST D
DIRECTIONS: Do not write on this test paper. Do all scratch work on thepaper provided to you for this purpose. Place all your answers on theanswer sheet. Do not spend too much time on any single problem.1. Which expression in the following list are not polynomials? Place the
letter preceeding the ,:orrect answer or answers on the answer sheet.
A. 3x E. 7
B. 4x2 - 2x + 5 -X
F. (x-7)(x+ 2)
x2+7x-3C. 3x2y + 2,xy2 - by + 4 G.
1 2-D.
5--x 2x + 4
x+ 1
H. x4 - 3x3 + 7x - 1
2. Which expression in the following list is a trinomial? Place the letter orletters preceeding the correct answer or answers on the answer sheet.
A. 4x 3 + 7x + 3
B. 2x
C. 7y 2 + 6
D. 9x 3 + 7x2 - 3x + 9
3. What is the degree of 3x5 - 2x4 + 7x - 3?
4. What is the degree of 4x3y + 6x2y - 3xy + 9x ?In problems 5-31, write the letter of the correct answer on the answer sheet.5. Arrange the following polynomial in descending order:
4x 2 + 4x3 + 5x - 3A. 4x3 - 3 + 4x2 + 5x
3.. -3 + 5x+ 4x2 + 4x
C. 4x3 + 4x + 5x - 3
B-77
153
6. ADD: (5x 2-6x+ 9) + (7x-4)
A. 5x 2 - 13x - 13
B. 5x2 + x + 5
C. 6x3 + 5
D. None of the above
7. ADD: 8x 3 - 2x2 + 5x - 33x3
+ 2x2 + 7x + 9
A. 11x 3 + 12x + 6B. 11x3 - 4x2 + 12x + 6C. 5x 3 - 2x 12
D. 5x3 + 12x + 6
8. SUBTRACT: (4x2-3x-2) - (2x2 -7x+ 3)
A. 6x2 - 10x + 1
B. 6x2 + 4x,- 5C. 2x2 - 10x + 1D. 2xz + 4x - 5
9. SUBTRACT: (2x3 -4x2 -7) - (2x2 -2x+3)
A. 2x3 - 2x 2 - Zx -4
B.3
- 6x2 + 2x - 10C. -4x2 - 2x - 10D. -4x2 + Zx - 4
10. SUBTRACT: 7x2y - 3xy2
3x2y - 3xy2
A. 10x2y - 6xy2
B. 4x y - 6xy2
C. 4x2y
D. None of the above
B- 78
154
11. What is the additive inverse of 3x2 - 2x + 4 ?
A. -3x2 + 2x- 4B. - 3x2+ 2x+ 4C. 3x2 + 2x -4D. 3x
2 - 2x + 4
12. Which of the following "laws" are incorrect?A. am an = am+n, where m and n are positive integers.
B. (ab)m = ab , m is a positive integer.C. (am
)n
= amn , in and n are positive integers.
13. SIMPLIFY: x3 x2 =
A. x6
B. x9
C. x5
14. (a5)2
A. al0B. a7
C. a2515 . 3
15. b
A. b5
B. b 18
C. b12
d916.
d
A. d12
B. d6
C.3
17. (xy)5 =
A. xy5
B. x5 y5
C. x5 y
D. None of the above.
18. (5x2y)2 =
A. 5x4 y2
B. 5x4y
C. 25x4 y2
D. 25x4y
19. (3:a2) (2a9)
A. 5allB. 5a18
C. 6a 18
D. ball20. (-5g 2)3
=
A. -125g 6
B. -125g8
C. -125g5
D. 125g5
21. (4x2yz3) (-2xy3 z2)
A. 8x2y3 z6
B. -8x3y4z
5
C. -8x y3 4z
6
D. 8x3y4z5
22. (3xt (-3xtv)A. -81x6t6v6
B. 81s8t8v8
C. 8 Is6t6v6
D. None of the above
B-8015
23. MULTIPLY: 3x2(5 -2x+ 7x2)
A. 15x2 - + 21x4
B. 15x2 - 6x3 + 21x4
C. 5x2- 6x.
3 + 21x4
24. MULTIPLY: 5y2 - 3y + 23y - 4
A. 15y3 - 11y2
+ 18y - 8
B. 15y3 + 29y 2
+ 18y - 8
C. 15y3 - 29y2+ 18y - 8
25. MULTIPLY: (4x-3) (5x+ 1)
A. 20x2 + 19x - 3B. 20x 2 - I9x - 3C. 20x 2 + 1 lx - 3D. 20x2 - I lx 3
26. MULTIPLY: (x-4)2
A. x2 + 8x + 16
B. x2 - 8x + 16C. x 2 - 16
D. x2 + 16
27. MULTIPLY: (2x+ 1)
A. 4x2+ 4x + 1
B. 2x 2 + 4x + 1
C. 4x2 + ID. 2x 2 + 1
2
28; D.IVIDEi* -51CI1-O-X7 if 5k
A. 2x4 + x3 + 5x
B. 2x 3 + x2 + 5
C. 2x 3 + x2 - x + I4 3 2
D. 2x + x - x + 5x
I 229. DIVIDE: x-7/ - 9x + 14
A. x + 2B. x - 2
C. x + 16 + x-7
D. x - 16 +x27
-98
30. DIVIDE: 2x-5 /6m3+ x2 - 18x - 33
A. 3x2 + 8x + 11 + 222x-5
-B. 3x2 - 7x + 9 +
2x23-5
C. 3x2 + 8x + 11D. None of the above
31. DIVIDE: 6x2-3 /12x5-12x 3+3x
-A. 2x3- 3x + x6
6x2-3
B. 2x3 x + -6x
C. 2x3 - 3xD. 2x
3 - x
6x2-3
32. COMPLETION: al =
33. COMPLETION: a° =
01.
, a= 034. The sum of 3 consecutive integers is 48. Determine the numbers.
UNIT VI Polynomials Test A B C D
NAME SECTION
TEACHER DATE
SCORE PERIOD
1. 18.
2. 19.
3. 20.
4. 21.
5. 22.
6. 23.
7. 24.
8. 25.
9. 26.
10. 27.
11. 28.
12. 29.
13. 30.
14. 31.
15. 32.
16. 33.
17. 34.
3-33
159
UNIT VU Special Products and Factoring Test A
DIRECTIONS: Do not write on this test paper. Do all scratch work on thepaper provided to you for this purpose. Place your answers on the answersheet. Do not spend too much time on any one problem.
1. Which of the following numbers is prime? Write the letter precedingthe number of the correct answer or answers on your answer sheetA. 1 C. 2
B. 9 D. 15
2. Factor 72 completely into powers of primes.
3. Give the second factor: 18x2y4 = 9xy ( )
4. Find the GCF of 12 and 18.
5. Find the GCF of 2x2y2 and 6x6 yz.
Factor completely all polynomials from number 6 through number 16.
6. 36x + 12y - 24
7. 25x3 - 15x2 - 5x
28. x --16
9. a2+ 8a + 16
1 0 . ba + 4b - 12
1.1 . 6c2 - c - 2
12. x3 - 3x2 + 7x - 21
13. 25x 2 - 81y
14. 2a3 + 20a2 + 50a
15. 2x2 - 8
16. -x2 + 2x - 1
17. Name the additive inverse of 4x2 - 5x - 7
18. COMPLETION: If a and b are numbers and (a)(b) = 0 but a 0 0,then 'a =
19. MULTIPLY: -1 (x` - 3x + 2) =
Solve each of the equations from number 20 through number 29. Write thesolutions to thcn-A on your answer sheet.
20. (x - 2) (x + 1) = 0
21. y(y - 2) = 0
22. (Za + 1) (a - 3) = 0
23. y2 - 25 z: 0
24.. y2 - 6y + 9 = 0
25. x2 + 3x = 10
26. 0(a - 2) = 0
27. 0(x - 7) 1
28. A man traveled 4 hours at x miles per hour, then at (20 + x) miles perhour for 3 hours. Represent the total distance traveled.
. B-85
161
UNIT VII Special Products and Factoring Test 13
DIRECTIONS: Do not write on this test paper. Do all scratch work on thepaper provided for this purpose. Place all answers on the answer sheet. Donot spend too much time on any one problem.
1 Which of the following numbers is not prime? Write the letter of thecorrect answer or answers on your answer sheet.A. 3 C. 2
B. 15 D. 5
2. Factor 68 completely into powers of primes.
3. Give the second factor: 45x2y5 = 9xy ( )
4. Find the GCF of 24 and 18.
5. Find the GCF of 3x3 y4 and 6x4y
4z.
Factor completely all polynomials from number 6 thru number 16.
6. 9x -.18y + 27
7. x2 25
8. 3x3 - 15x - 42x
9. a2 + 12a + 36
1 0 . bz + b - 12
11. 6d2 + 3d - 3
12. x3 - 7x2 + 3x - 21
13. 9x2
- 64y2
14. 3a3 + 21a2 - 48a
B-36
162
15. 3x 2 - 27
1 6 . -x2 + x + 6
17. COMPLETION: If a and b are numbers and ab = 0 and b # 0, thena=
18. MULTIPLY: -1 (2 - 5x - 2)
19. Name the additive inverse of -6x2 + 5x + 4.
Solve each of the equations from number 20 through 27. Write the solutionson your answer sheet.
20. (a - 3) (a + 4) = 0
2 1 . (2a - 1) (a - 4) = 0
22. t(t - 3) = 0
23. x2 - 16 = 0
24. X2 - 10x + 25 = 0
25. a2 + 5a = -6
26. 0(t + 3) = 0
27. 0(a - 3) = 1
28. The sum of 3 consecutive integers is 39. Determine the three integers.
B-37
163
UNIT VII Special Products and Factoring Test C
DIRECTIONS: Do not write on this test paper. Do all scratch work on thepaper provided to you for this purpose. Place your answers on the answersheet. Do not spend too much time on any one problem.
1. Which of the following numbers is prime? Write the letter precedingthe number of the correct answer or answers on your answer sheet.A. 6 C. 1
B. 5 D. 9
Z. Factor 84 completely into powers of primes.
3.
4.
5.
Give the second factor:
Find the GCF of 12 and 15.
Find the GCF of 3a2b2 and 6a6bc
16a2b
4 = 8ab (
Factor completely all polynomials from number 6 through 16.
6. 18x + 12y - 24
7. 20x3 - 15x2 + 5x
8. xz - 81
9. y2 + lly + 16
10. r 2 + 7r - 30.
11. 15yz -
12. a 3 - 3a2 + 5a - 15
13. 36r2 - 81s 2
3 214. x - 2x + x
B-88
1$4
15. 4c 2 - 16
16. -a2 + 2a - 1
17. Name the additive inverse of 6a 2 - 3a - 1.
18. COMPLETION: If a and b are numbers and (a)(b) = 0, but b # 0,then a =
19. MULTIPLY: -1(y2 - 5y + 3)
Solve each of the equations from number 20 through number 29. Write thesolutions to them on your answer sheet.
20. (a + 1) (a - 3) =
21. x(x - 10) = 0
22. (2a + 3) (a - 1) = 0
23. x2 - 81 = 0
25. r2 + 5r = 6
26. 0(x + 5) = 0
27. 0(a 8) = 1
28. Two jet transports start at the same time from the same airport. Oneflies due east at 620 miles per hour. The other flies directly west at560 miles per hour. In how many hours will they be 3540 mUes apart.
B-89
165
UNIT VII Special Products and Factoring Test D
DIRECTIONS: Do not write on this test paper. Do all scratch work on thepaper provided to you. Place your answers on the answer sheet. Do notspend too much time on any one problem.
1. Which of the following numbers is prime? Write the letter of the correctanswer or answers on your answer sheet.A. 7
B. 5
C. 4
D. 6
2. Factor 56 completely into powers of primes.
3. Give the second factor: 28x2y5 = 7xy ( j
4. Find the GCF of 16 and 24.
5. Find the GCF of 3x2y3 and 12x5y2z.
Factor completely all polynomials from number 6 through number 16.
6. 25x + 5y - 10z
7. 36x 3 + 24x2 + 12x
8. x2 - 36
9. y2+ 6y+ 9
10. b2 + 5b - 14
11. 6c2 + c - 2
12. x3 - 5x2 + 2x - 10
13. 49x2 81y2
14. 4a3 + 40a2 + 100a
B- 90
166
15. 3x 2 - 27
1 6 . -x2 - 2x - 1
17. Name the additive inverse of -9x2 + 3x - 6.
18. MULTIPLY: -1(x 2 + 6x - 7) =
19. COMPLETION: If x and y are numbers and (x)(y) = 0 but x 0, thenY
Solve each of the equations from number 20 through number 27. Write thesolutions to them on your answer sheet.
20. (x + 6) (x - 7) = 0
21. y(y - 3) = 0
22. (3a + 2) (a - 3) = 0
23. y2 - 81 = 0
24. y2 + 1 Oy + 25 = 0
25. lc2 - 5x = 36
26. 0(a + 7) = 1
27. 0(a - 8) = 0
28. A number increased by three is equal to twice that, same numberdecreased by 1. Determine the number.
B -91
167
UNIT VII Special Products and Factoring Test A BCD
NAME SECTION
TEACHER DATE
SCORE PERIOD
1. 15.
2. 16.
3. 17.
4. 18.
5. 19.
6. 20.
7. 21.
8. 22.
9. 23.
24.
11. 25.
12. 26.
13. 27.
i4. 28.
B-92.
leg
Unit VIII FRACTP.;.NS Part ITest A
DIRECTIONS: Do not write on this test paper. Do all work on the scratchpaper provided to you. Place all answers on the answer sheet. Do notspend too much time on any one problem.
In problems 1 through 5, determine the values of the variable for which thefraction is not defined. If there are no exclusions, write "none".
1.
2.
5
x
7x-3
2x + I3. x +
4.
5.
7x -24
x2 +
x2 - 4
6. COMPLETION: An algebraic fraction is the indicatedof two real numbers, polynomials, or combinations of these.
37. COMPLETION:.4
In the fraction , 3 is called the(numerator, denominator).
Reduce the fractions in problems 8 through .13 to lowest terms. If thefraction is already in simplest form, write "done" on your answer sheet.
368.
9.
10.
11.
42
20a 2b
25ab 2
80x2yz
15xy 2z
x + 3x2 - 9
B-93169
12.
13.
x2 + 2x + 1
x2 x - 2
aba +b
In problems 14 through 18, give the products reduced to lowest terms.x
14.2
63 xy
15x15. (7xy) (
14y ) -
7(x - y) 8x5 y - x
a2 - b2 m -m + n a + b
a 2 + 5a + 4 a + 5a+ 4 a2+ 6a + 5
In problems 19 through 24 give the quotient reduced to lowest terms. Assumethat there are no divisions by zero.
5 -319.
6 4
15x20. 16y ÷ 5x =.
521. 7x 2y 2x
2a. 15a2 25a3
7b 14b2
23.3x+ 6 x2 + 5x + 62 2 x + yx - y
3a 6a + 4 a + 23a + 2 4a 2
25. Jim and Joe earned a total of :36. Joe earned :;.3 more than one -halfof what Jim. earned. HoW much did each earn?
B-94
Unit VIII FRACTIONS Part ITest B
DIRECTIONS: Do not write on the test paper. Do all work on scrap paperand place final answers on the answer sheet. Do NOT spend too much timeon any one problem.
In problems 1 through 5, determine the values of the variable for which thefraction is not defined. If there are no exclusions, write "none".
1. x+ 1
2.3
x - 2
3.2x + 1
4.x + 4
2x 25
5.3x - 7
9
6. Completion: An algebraic fraction is the indicatedof two real numbers, polynomials or combinations of the same.
37. Completion: In the fraction 4 , 4 is called the
(numerator, denominator).
Reduce the fractions in problems 8 through 13 to lowest terms. If thefraction is already in simplest form, write "done" on your answer sheet-
8.7 2
9. 220a b15ab 2
2z210. 20xyz
B -95
171
31.
12.
13. 2+ b
x +5
x2 - 25
x2+ 4x + 4
. - x - 6
2a
In problems 14 through 18, give the product or quotient reduced to lowestterms.
14 51-3226 x
15. (3xy) (4x )9,-
16.3 (a - b) 8x
8 9 (b - a)
a - b17.
a2 - b2 x2 2_y
18.c
2 + 3c + 2c + 1
c + 1
c2+ 5c + 4
In problems 19 through 24, give the quotient reduced to lowest terms. Assumethat there are no divisions by zero.
5 -39 5
19.
20.18x + 6x21y
21. 7x2y +5xZy
22.21a2 7a 3
9b 3b2
23.4x+ 20 x+ 5
x2 - 4y 2 x - 2y
24.
7X - 1 x X + 1
- 1 5x2
25. A rectangle is 2 yards longer than it is wide. The area of the rectangleis 99 square yards. Find its dimensions.
Unit VIII FRACTIONS Part ITest C
DIRECTICNS: Do not write on this test paper. Do all work on the scratchpaper provided to you. Place all answers on the answer sheet. Do not spendtoo much time on any one problem.
In problems 1 through 5, determine the value of the y;ariable for which thefraction is not defined. If there are no exclusions, write "none".
53.
4.
5.
x2 + 5
x2 - 9
7y + 14
6. Completion: In the fraction , 7 is the (numerator,denominator ).
7. True or False: An algebraic fraction is the indicated quotient of tworeal numbers, polynomials or combinations of these.
Reduce the fractions in problems 8 through 13 to lowest terms. If thefraction is already in simple form, write "done".
38.
38
9.
10.
50
36a2b3
16ab
15x4y2z
345x6yz
B -97
12.
13.c2- 9
x - 7x2 - 49
cz + 66+ 9
In problems 14 through 18, give the products reduced to lowest terms. Assumethat there are no divisions by zero.
14. (8 x y) (4x )
a3 1215,
4 ab
16.
17.
18.
9(a b) 5A b - a
a2 + a 62 a2- 1
x2 ..5x + 6 x + 3x- 2 x2 - 9
In problems 19 through 24 give the quotient reduced to lowest terms. Assumethat th:re are no divisions by zero.
3 -127 7 5
19.
20.
21.
22.
23.
24.
21x- 3z
16y
3 4x18x y+
24a3 8a27b 21b3
x2 + 4x +3
x + 2x z + x - 6
x + 2
xz lox + 25. x + 5x+ 10 x2+ + 10+ 15x+ 50
B-98
25. An object is thrown from a plane at an altitude of 000 ivc.t, ti thcrobject falls at a rate of 52 feet per second, how lone, will it take for theobject to reach the ground?
B- 99
175
Unit VIII FRACTIONS Part ITest D
DIRECTIONS: Do not write on this teat paper. Do all work on the scratchpaper provided to you. Place all answers on the answer sheet. Do notspend too much time on any one problem.
In problems 1 through 5, determine the values of the variable for whichthe fraction is not defined. If there are no exclusions, write "none".
1.
2.
3.
4. 5x -35
x2+ 15.
x2 - 46. Completion: An algebraic fraction is the indicated
of two real numbers, polynomials, or combination of these.57. Completion: In the fraction 12 is called
(numerator, denominator).
Reduce the fractions in problems 8 through 13 to lowest terms. If thefraction is already in simplest form, write "done" on your answer sheet.
8.
9.
10.
ii.
2442
10x_y:
60a2bc
25abc2
x + 2..1c2 - 4
8-100
1.?E;
12. JD
2413 + 3
p2 + 3p - 4
13. 2-11-X - y
In problems 14 through 18, give the products reduced to lowest terms.2
814. y----2 xy
15z15. (6 x z) (12x )
16. 5(a b) 8a7 b - a
2 2 2 2w vw + v x + y17,
18.a 2 - 12a + 32 a 2 - 16
a + 4 a - 8
In problems 19 through 23, give the quotient reduced to lowest terms. Assumethat there are no divisions by zero.
19.5
--zr--34
12x20. 14y + 6x
521. 8x2y 4x
22.15z
214w 2
7w 25z 3
23.
24.
3a + 6a2 - b2
+ 2x+ 1 2x+ 6 x+ 1
a2+ 5a + 6a + b
3x 6x3 12x 3
25. A rectangle is 8 feet longer than it is wide. Its area is 105 square feet.Find its dimensions.
UNIT VIII
NAME
TEACHER
SCORE
Fractions
1. 17.
2. 18.
3. 19.
4. 20.
5. 21.
6. 22.
7. 23.
8. 24.
9. 25.
10.
11.
12.
13.
14.
15.
16.
8-102
178
PART I ABC DSECTION
DATE
PERIOD
UNIT VIII Fractions PART IITest A
DIRECTIONS: Do not write on this test paper. Place all answers on theanswer sheet. Do not spend too much time on any one problem.
In Problems 1 through 10, give the sum or difference reduced to lowest terms.Assume that there are no divisions by zero.
1.
2.
3.
4.
5 2+ 9
x 3
5 5
2 - 3ab
5 37 + 4 =
52a 3a5 4
6. a2 4a - 2 a - 2
1111111
10x x2 + 257. + x + 5 =x + 5
78 - 3
a2 ab2
x 49. x2 - 81 x + 9
1 0 .x - 1 x+ 2
xx - 2x - 8 2 + x - 2
11. SIMPLIFY:
5x6
10x12y
B-103
179
a+ 1
12. SIMPLIFY:a
13. What is the ratio in lowest terms of 6 feet to 4 yards?
In Problems 14 through 21, solve each equation or inequality and write thesolution on the answer sheet:.
14.
15.
16.
17.
x x 3
3 + 4
2m - 1 2 - m5 5
x -4 5
2c 3c+ 1 <
18.2 : 3z
5 2
19.
20.
3 7
4 x
9 6
a +2 a +2
60 5
a21. + 1 =
2 -36
1
a - 6
B-1 04
180
UNIT VIII Fractions PART IITest B
DIRECTIONS: Do not write on this test paper. Place all answers on theanswer sheet. Do not spend too much time on any one problem.
In Prob/ems 1 to 10, give the sum or difference reduced to lowest terms?Assume that there are no divisions by zero.
1.
2.
4 27+7x 5
8 8
b 3 - 2b3.
4 24
+
3a 5a5.
5 -F 6
6.x2 9x - 3 x - 3
7. 12x x2 + 3 6x + 6 x + 6
5 28.
azb a b
x 3
x9 +2 -49 x + 7
i
x - 2 x + 22
10. + 2x - 3x - 4 x
11. SIMPLIFY.
4x58x
1 Oy
B-105
12i
12. SIMPLIFY:
13. What is the ratio in lowest terms of 6 feet to 4 yards?
In Problems 14 through 21, solve each equation or inequality and write thesolution on the answer sheet.
14.
15.
16.
x x 3
+ 5
3m - 25
x x- 35
=6
3 - m5
317. -5c + 1 < 4c
-18 .5
6 - 5y
19. 6+
4=x 5
20. 8 5- -a 3 a - 3
40 5
a21. + 1 =
2 - 16 - 4
1
UNIT VIII Fractions PART 11Test I)
DIRECTIONS: Do not write on this test paper. Place all answers on theanswer sheet. Do not spend too much time on any one problem.
In Problems 1 through 10, give the sum or difference reduced to lowest terms.Assume that there are no divisions by zero.
1.
2.
3.
4.
5.
6.
8.
9.
10.
5 2
4. 4
x 5
8 8
a 2 - 3ab b
4 25
Za 3a5
2
x -3 x - 3
xi + 2510xx + 5 x +5
5
alb a2
4
x2 - 81 x + 9
x - 2 x + 2x - 3x -4 xi - x - 2
11. SIMPLIFY:5x6
10x12y
B-107
183
A12. SIMPLIFY: B
A+ 1
13. What is the ratio in lowest terms of 6 feet to 4 yards?
In Problems 14 through 21, solve each equation or inequality and write thesolution on the answer sheet.
14. x x 3
7 "I' 5 2-- 7
15. 2y - 1 2 - y5 5
16. z - 35 6
3d17. 2d+ 1 <
8x 6 - 5x18. >85 2
5 3 719. + =x 4
20. 8 5a + 3 a + 3
1
60 5
a21. + 1
2 -36 a - 6
B-108
i8
UNIT VIII Fractions PART IITest D
DIRECTIONS: Do not write on this test paper. Place all answers on theanswer sheet. Do not spend too much time on any one problem.
In Problems 1 to 10, give the sum or difference reduced to lowest terms.Assume that there are no divisions by zero.
4 2+ 7
1.
2.x 3
5 5
3b 3 - 2b
.
4.5 3
+
53a 5a5 6
6.
8.
a2 4a - 2 a -2
I 2x x2 + 36x+ 6 x + 6
7
alb ab2
9 . +3
.x - 49 x+ 7
10.x - I x + 2
x2 - 2x - 8 x2 +x -24x
11. SIMPLIFY: 5
1 Oy
B-109
185
12. SIMPLIFY:1
13 . What is the ratio in lowest terms of 4 feet to 4 yards?
In Problems 14 through 21, solve each equation or inequality and write thesolution on the answer sheet.
14
15.
16.
1?.
x x 3
3 4. 4
3m - 25
x - 24 5
3 - m - 15
5c3
+ 1 <-4
c
18'.5 2
19. 6 4 5x 5 x
620. 9 -a - 2 a -2
21.40
+az - 16
5
a - 4
B-110
1
UNIT VIII
NAME
TEACHER
SCORE
Fractions PART IITestABCD
SECTION
DATE
PERIOD
1. 12.
2. 13.
3. 14.
4. 15.
5. 16.
6. 17.
18.
8. 19.
9. 20.
10. 21.
11.
B-111
UNIT IX Graphs and Sentences in Two Variables PART ITest A
DIRECTIONS: Do not write on this test booklet. Do all scratch work onthe paper provided for this purpose. Place your answers on the answer sheet.Do not spend too much time on any one problem.
Fill in each numbered blank with the letter preceding the word from the followinglist that makes each sentence correct.
A.
B.
t--,.....
D.
E.
coordinate axes
quadrant
ordered pair
coordinates
ordinate
F.
G.
H.
I.
J.
origin
abscissa
line
point
variable
The major horizontal and vertical lines in a Cartesian Axis System arecalled (11 . The point where they intersect is called the
(2) of the system. Each point in the plane is locatedby attaching two numbers to it called the (3) of thepoint. These two numbers are usually written so that the order is important.Hence, the pair is called a(n) (4) . The first number of thepair is called the (5) of the point, and the second number iscalled the (61 of the point. The plane is divided into fourprincipal regions by the major lieeoe. Each of these regions is called
(7)
8. Write the letter of the correct answer on the answer sheet. The pointA(-7, 3) lies in quadrant:A. I D. TV
B. II
C. III
E. None
9. Write the letter of the correct answer on the answer sheet. The pointEl(-7, 0) lies in quadrant:A.
B. II
C. m
B-112
1 8
D. IV
E. None
10 TRUE or FALSE: The point C(5, 0) lies on the x-axis
11 TRUE or FALSE: The point I(0, 0) lies in the y-a:ds.
12 TRUE or FALSE: The point P(2 a) lies in quadrant IV if a < 0
13 COMPLETION: Consider the expression x23. The number
is the subsc :ipt
Solve each of, the equations in numbers 14 through 16 for y in tern's of x
14 2y 3x- 1
15. Zx - 2.y -I. 1 0
16 7x -I. 3y - 4 0
17 Consider the equation 5x - 3y + 2 = 0 If x = 4, then
18. Graph the following points and label them properly. Use theCartesian System given on your answer sheet. All must be plottedproperlyA A.(-3,2) C. C(0, -2)
B. 13(4, 0) D. D(-2; -3)
19. Using the Cartesian System given on your answer sheet, graph theequation:
- 2y + 1 = 0
Use the chart method. Complete the chart that appears on youranswer sheet
20 Examine the graph given below. What is the v- intercept of the line
13-113
189
21. What is the y-intercept of the graph of the 'tine whose equation is- 4) (a 0 ?
22. Graph the line whose equation is x = -.2 in the given Cartesian System.
23. Graph the line whose equation is y = 2 on the given Cartesian System.
24. COMPLETION: is the equation of the x-axis.
25. Which one or ones of the following equations is (are) linear. Write theletter preceding the correct answer (s) on the answer sheet.A. 1 "= ..
Y
3x - 2
5: - -1- 3
.1) 2x - 3y 6 - ()
E. None of these.
26. What is the slope of the line given by the graph below')
......
r. -. . -.4.1 Fl 111111
.1Elli111111.4.111.
4,--4
111111111111111111M
1....4._
bi.i)
--1-
OPi
L i
-i- ...1..
i-I..
1 i
L.i...1 ! ........
-!
(---->27. What: is the slope of the line A.- B if A has the coordinates (-3,-2) and
B has the coordinates (5, 7) ?
Z3. Whi,:11:.)f the lines defined by the equations below have no slope definedfor it? Write the letter of the correct answer on your answer sheet.A. x .= 4 23( - 3y + 5= 0
B. y 2
B -1 14
1). All of the above haveslopes defined.
UNIT IX Graphs and Sentences in Two Variables PART ITest B
DIRECTIONS: Do'not write .on this test booklet. Do all scratch work onthe paper provided for this purpose. Place your answers on the answer sheet.Do not spend too much time on any one problem.
Fill in each numbered blank with the number preceding the word from thefollowing list that makes each sentence correct.
A. Ordinate F. Variable
B. Coordinate axes G. Origin
C. Coordinates H. Point
D. Line I. Quadrant
E. Ordered pairs J. Abscissa
The major horizontal and vertical lines in the Cartesian Axis system arecalled The point where they intersect is called the
(2J . Each point in the plane is located by attaching twonumbers to it called the DJ of the point. These two numbersare usually written so that the order is important. Hence, the pair is calleda(n) (41 . The first number of the pair is called the (5)of the point, and the second number is called the (6) of the point.The plane is divicled into four principal regions by the major lines. Each ofthese regions is called a(n) (7)
8. Write the letter of the correct answer on the answer sheet. The point(7, -3) lies in quadrant:A. I D. IV
B. II E. None
C. III
9. Write the letter of the correct answer on the answer sheet. The point(6,0) lies in quadrant:
B-115
191
t. IV
E. None
.MIMOTTY.11.111111611111111.0..-a-
10. TRUE or FALSE: The point (5, 0) lies on thi7 y-axis.
11. TRUE or FALSE: The point 1(0, 0) lies on the x-axis.
12. TRUE or FALSE: The point P(«., 1) lies in quadrant II if a <0.
13. COMPLETION: In xi 3 the number is thesubscript.
Solve each of the equations a numbers 14-16 for y in terms of x.
14. 4y = 3x - 1
3x -1- 2 y =
16. 8x + 3y = 0
17. Consider the equation 5x - 3y + Z = 0. x = 2, then y =
18. Graph the following points and label. them properly. Use the CartesianSystem on your answer sheet. ALL must be plotted correctly.A. A(3,-.2)
B. B(6,0)
C. C(0,-3)
D. D(-2.,-3)
19., Using the Cartesian System given on your answer sheet, graph thethe equation 2x y 3 = 0. Use the chart method. ez;mplete thechart that appears on your answer sheet.
20. Examine the graph given below. What is the x-intercept of the line?
13 -116
192
21. What is the y-intercept of the graph of the line, whose equationis 2x 7,r + 14 ?
22. Graph the line whose equation is x -3 in the given system.
23. Graph the line whose equation is y = 4 on the given Cartesian System.
24. COMPLETION: is the equation of they-axis.
25. Which of the following are linear? Write the letter preceding thecorrect answer on the answer sheet.A.
B.
Y
Y
4x .4- 2
5x"
C. y = 6x2 + 4x + 3
D. 3x - 4y + 6 = 0
E. None of these.
26. What is the slope of the line given by the graph below?
4, Tr-
-4-.t
iI
1
;la
PAlIFi
InU
1111
;
i--
InA4
isfato.
.
Li7
armIs
I IIa! aL / ail
7
27. What is the slope of line AB if A has the coordinates (3, -2) andB has the coordinates (5, ?
28. Which of the lines defined by the equations below has.reno slope definedfor it? Write the letter of the correct answer on the answer sheet.A. x= 6B. y = 5
C. 3x - + 5 = 0D. All of the above have
slopes defined.
UNIT IX Graphs and Sentences in Two Variables PART ITest C
DIRECTIONS: Do not write on this test booklet. Do all scratch work on thepaper provided for this purpose. Place your answers on the answer sheet. Donot spend too much time on any one problem.
Fill in each numbered blank with the letter preceding the word from thefollowing list that makes each sentence correct.
A. ordered pair. F. abscissa
B. quadrant G. variable
C. coordinate axes H. point
D. coordinates I. ordinate
E. origin J. line
The mak-vr horizontal and vertical lines in a Cartesian Axis System arecalled (1 . The point where they intersect is called the
(2) of the system. Each point in the plane is located byattar-hing two.nambers to it called the (3) of the point. Thesetwo numbers are usually written so that the order is important. Hence, thepair is called a(n) The first nr.aber. of the pair is calledthe (5) of the point and the second number is called the
(6) of the point. The plane is divided into four principalregions by the major lines. Each of these regions is called a(n) (7)
8. Write the letter of the correct answer on the answer sheet. The pointA(8, -2) lies in quadrant:A. I D. IV
B. II E. 1tonne
C. III
9. Write the letter of the correct answer on the answer sheet. The pointB(0, -5) lies in quadrant:A. I D. IV
B. II
C. III
E. None
10. TRUE or FALSE: The point C(-3, 0) lies on the x- axis!.
194
1.1.. TRUE or FALSE: The 'pOint 1(0,0) lies in the x-axis.
12. TRUE or FALSE: The point P(,3,a)lies in.quadrant.II if.a < 0.
13. COMPLETION: Consider the expression x32. The
number is the subscript.
Solve each of the equations in numbers 14 through 16 for y in terms of x.
14. 3y = Zx + 1
1 5 . 3x - 3y + 1 = 0
1 6 . 10x+ 3y- 4 = 0
17. Consider the equation 5x - 3y + 2 = 0. If x = 5, then y
18. Graph the following points and label them properly. Use the CartesianSystem even on your answer sheet. All must be plotted properly.A. A( -5, 1)
B. 13(3,0)
C. C(0,-3)D. r)(-1 , -2)
19. Using the Cartesian System given on your answer sheet, graph theequation 2x - y 1 = 0. Use the chart method. Complete the chartthat appears on your answer sheet.
20. Examine the graph given below. What is the y-intercept of the line?
UMN MUOME II 0 MAIM iMOI NM
Irli
MUJOI
lagrillME
MoWrn
anM
IIMEMMNIMMIminitilin
U
AM
10.
fU
1-{i ! !
21. What is the y-intercept of the graph of the line whose equation is2x - 3y + 5 = 0 ?
13-119
195
22. Graph the line whose equation is in thy; given system.
23. Graph the tine whose equation is x = 3 on the given Cartesian System.
24. COMPLETION: is the equation of the
25. Which one or ones of the following equations is (are) linear? Writethe letter preceding the correct ansv..er(s) on the answer sheet.
y = 2x+ 12
13. y = 5x 4x 1-3
C. 2x- 3y + 4 = 0
D. y 6x2
26. What is the slope of the line given by the graph below?
F I
J.
27. What is the slope of the line AB if A has the coordinates (-4, -2) andB(5,8) ?
28. Which of lines defined by the equations below has no slope defined forit? Write the letter of the correct answer on your answer sheet.A. y = 2 C . x = 4
B. 2x - 3 y 5 = 0 D . All of the above haveslopes.
196
UNIT IX Graphs and Sentences in Two Variables PART ITest D
DIRECTIONS: Do not write on this test booklet. Do all scratch work onthe paper provided for this purpose. Place your answers. on the answer sheet.Do not spend too Inuch time on any one problem.
Fill in each numbered blank withfollowing list that makes each sentence
the letter preceding the word fro thecorrect.
A. origin F. point
B. coordinate axes G. quadrant
C. variable H. ordinate
D. ordered pair I. line
E. abscissa J. coordinates
The major horizontal and vertical lines in a Cartesian Axis System arecalled (1) . The point where they intersect is called the
2 of the system. Each point in the plane is located byattaching two numbers to it called the (3 of the point.These two numbers are usually written so that the order is important, Hence,the pair is called a(n) (4.) . The first number of the pair iscalled the of the point, and the second number is calledthe (6) of the point. The plane is divided into fourprincipal regions by the major lines. Each of these regions is calleda(n) (7)
8. Write the letter of the correct answer on the answer sheet. The pointB(3, 0) lies in quadrant:A. 1 D. IV
B. II E. None
C. III
9. Write the letter of the correct answer on the answer sheet. The pointA(-3, -5) lies in quadrant:A.
B. II
B-121
197
D. IV
E. None
10. TRUE or...FALSE.:
11 . TRUE or FALSE:
12. TRUE or FALSE:
The point C(0, 3) lies on the x-axis.
The point A(0, 0) lies on the y-axis.
The point P(5, a) lies in quadrant Ii if a < 0.
13. COMPLETION: Cons:ide.r the expression x47. The numberis the subscript.
In Problems 14-16, solve each of the equations for y in terms of x.
14. 5y = 6x - .1
15. 3x- 2y + 5 0
16. 9x + 4y 9 = 0
17. Consider the equation 7% - 2y 5 = O. if x = 3, then y
18. Graph the following points and label them properly. Use the CartesianSystem given on your answer sheet. All must be plotted properly.A. A(-6,-5)
I3( -3, 4)
C. C(0,2)
.D. D(-5, 0)
19. Using the Cartesian System given on your answer sheet, graph theequation x 2,, 3. Use the chart method. Complete the chart thatappears on your answer sheet.
20. Examine the graph given below. What is the y-intercept of the line?1
_
a All
a # IVANRae FA
rd
gal =reLIM
moilimmiliim,
WI IIB -122
21. What is the y-intercept of the graph of the line whose equation is7x - 5y+ 4_. 0 ?
22. Graph the line whose equation is y = -3 on the given CartesianSystem.
23. Graph the line whose equation is x = 2 on the given Cartesian System.
24. TRUE or FALSE: x = 0 is the equation of the y-axis.
25. Which one or ones of the following equations is (are) linear? Writethe letter of the correct a.nswer(s) on the answer sheet.A. y == 4x + 2
y = 3x2 - I
C. 2y + 3x z 1
D. None of these.
26. What is the slope of the line given by the graph below?
11 iniII SUSISIENINS
111M1111.1111rILOS
umIN
anarauni
1111111111110CUIIIIIIIIIIIIII Imum Nuirarigi--4--t-
111111011111=11111111111111W11 Ms
MN as
27. What is the slope of the line AB if A has the coordinates A(4, -2)and B has the coordinates (6,8) ?
28. Which of the lines defined by the equations below have no slope definedfor it? Write the letter(s) of the correct answers) on your answersheet.A. y= 5B. 3x + ly -- 7
B-123
99
C. x = -2D. All of the above have
slopes.
UNIT IX
NAME
Graphs and Sentences in Two Variables PART ITestABCD
TEACHER
SCORE 11. 18.
2.
3.
4.
5.
6.
7.
8.
910.
12.
13.
14.
15.
16.
17.
B-124
202
SECTION
DATE
PERIOD
11111111111101N1111111111111111MON1111111111.
11111111111111111111111111111111i
111110 11111111111111MME
MOM RE1111111111111inol11111111111HUMBM1111111111111111111111111111
11111111111111111111111
111111111M111111111111111111 111111111111111111111111
11P RI 1111111111
111111111111111111111111 Ed HM/
IMMIUMINEMPINUMMOIMO MUMmRiNniOnliniii
1M1111111111111111111111MMIIII
1111111111111111111111OWNIIII1111111111111
x -3 -1 +3
20.
21.
22.
23.
24.
25.
26.
27.
28.
B-125
201
,4 WI.
UNIT IX Graphs and Sentences in Two Variables PART IITest A
DIRECTIONS: Place all answers on the answer sheet provided to you. Donot write on this test booklet. Do all scratch work on the paper provided forthis purpose. Do not spend too much time on any one problem.
1. COMPLETION: If a line runs downhill from left to right, its slopeis (negative, positive).
Z. Plot the line determined by the points C(.3, 2) and D(2, 0) on the givensystem.
3. What is the slope of the line whose equation is y = 3x - 1 ?
4. What is the slope of the line whose equation is 3x + 2y - 6 = 0 ?25. Plot the line through the point A(2, -1) with slope m = 3 on the given
system.
6. Plot the line whose y-intercept is -2 and whose slope is -1 on thegiven system.
7. Plot the line whose equation is y = 3x - 2 on the given system.
8. Plot the line whose equation is 2x - 3y + 6 = 0 on the given system.
9. A line has a slope of -2 and a y-intercept of +1. Write its equation.
10. A line has a slope of +3 and goes through A(2,1). Write its equation.
11. A line is determined by the two points A( -3, 2) and B(2,-3). Writeits equation.
12. Graph the inequality x > 2 on the given system.
13. Graph the inequality y < 1 on the given system.
14. Graph the inequality u. - y <1 on the given system.
15. Graph y = x2 on filo given system.
16. Plot both of the lines whose equations are given below on the same givenset of axes and determine the common solution, if one exists.
5x - y 0
x + y - 3 = 0
B-126
2n2
17. Consider the system of equations:y = -2x + 1 and 5x + 3y = 5
Find the common solution to the system, if one exists.
18. Find the common solution to the following system of equations, ifone exists.
2x - 5y = 4.
3x + 4y = -17
19. EVALUATE: 42
2L. EVALUATE:
21.
Ar
1-1
3
7 I
35 I
Consider the system: 5x 2y+ 3 = Li
2x- Ty + 9=The expression: 5
2 -991
5 -22 -7
gives the (x or y) value of the common solution.
B-127
203
UNIT IX Graphs and Sentences in Two Viriables PART IITest B
DIRECTIONS: Place all answers on the answer sheet provided to you. Donot write on this test booklet. Do all acratchwork on the paper provided forthis purpose. Do not spend too much time on any one problem.
1. COMPLETION: If a line runs uphill from left to right, its slope is(positive, negative).
2. Plot the line determined by the points C(-3,1) and D(3, U) on the givensystem.
3. Vv hat is the slope of the line whose equation is y = 5x - 1 ?
4. What is the slope of the line whose equation is 4x + 3y - o = 0 ?
5. Plot the line through the point A(3, -1) with slope in = 3 on thegiven system.
6. Plot the line whose y-intercept is -3 and whose slope is -1.
7. Plot the line whose equation is y = 2x - 3.
8. Plot the line whose equation is 2x - 3y + 6 = C.
9. A line has a slope of -2 and a y-intercept of 2. 'Write its equation.
1U. A line has a slope of 3 and goes through the point C(3, 1). Write itsequation.
11. A line is determined by the two points A(- 3, 2) and B(2, -3). Writeits equation.
12. Graph the inequality x > 3 on the given system.
13. Graph the inequality y < -1 on the given system.
14. Graph the inequality x - y <1 on the given system.
15. Graph y = x2 on the given system.
/6. Plot both of the lines whose equations are given below on the same givenset of axes determine this common solution if one exists.
5x - y - 9 =
2 x + y - 5 =
B-123
2 n 4
17. Consider the system of equations y a -2x + T and 2x + 3y 13.Find the common solution if one exists.
18. Find the common solution to the following system if one exists,
2x - 5y = 43x+ 4y= -11
19. EVALUATE: 7 48
20. EVALUATE: -3-1
34
21. Consider the system: '7x + 2y + 3 =2x + Ty + 9=
The expression:127 :391
172 271
gives the x or y) value of the common solution.
UNIT IX Graphs and Sentences in Two Variables PART IITest C
DIRECTIONS: Place all answers on the answer sheet provided to you. Don...t write on this test booklet. Do all scratch work on the paper provided forthis purpose. Go not spend too much time on any one problem.
1. COMPLETION: If a line runs downhill from left to right, its slope is(negative, positive).
2. Plot the line determined by the points C(-I,3) and D(2, -2) on the givensystem.
3. What is the slope of the line whose equation is y = -2x + 5?
4. What is the slope of the line whose equation is 5x + 3y + 9 = 0 ?15. Plot the line through the point B(-2, 3) with a slope of 3 on the
given system.
6. Plot the line whose y-intercept is 2 and whose slope is -2 on the givensystem.
7. Plot the line whose equation is y = 2x + 4 on the given system.
8. Plot the line whose equation is 3x - 4y + 8 = 0 on the given system.
9. A line has a slope of 4 and a y-intercept of -3. Write its equation.
10. A line has a slope of -2 and goes through C(1, 3). Write its equation.
11. A line is determined by the two points C(0, -2) and D(3, 4). Write itsequation.
12. Graph the inequality y < I on the given system.
13. Graph the inequality x > 3 on the given system.
14. Graph the inequality 2x - y > 2 on the given system.
15. Graph y = x2 on the given system.
16. Plot both of the lines whose equations are given below on the same givenset of axes and determine the common solution, tf one exists.
2x + y- I = 0x+ y- 3= 0
13-130
20E
17. Consider the system of equations: 2x 3y a 1 and4y a 3x
Find the common solution to the system, if one exists.
18. Find the common solution to the following system of equations, if oneexists.
3x + 2y= 5 andx - y = 5
19. EVALUATE: 4 -21
20. EVALUATE:4
1-6-311
21. Consider the system: 2x + y - 1 = 0 and5x + 3y - 5= 0
The expression:115 311
11
5 31
gives the (x or y) value of the common solution.
B-131
207
UNIT IX Graphs and Sentences in Two Variables PART IIT'et D
DIRECTIONS: Do not write on this teat booklet. Do all scratch work onthe paper provided for this purpose,. Place your answers on the answersheet. Do not spend too much time on any one proolem.
1. COMPLETION: if a line runs uphill from left to right, its slope is(positive, negative).
2. Plot the line determined by the points C(-3.4) and D(4, 0) on the givensystem.
3. What is the slope of the line whose equation is y = 7x - 1 ?
4. What is the slope of the line whose equation is 3x + 5y - 8 = 0 ?
5. Plot the line through the point A(3, -1) with slope in 34 or.: the given3system.
6. Plot the line whose y-intercept is -2 and whose slope is -2.
7. Plot the line whort. equation is y = 4x - 2.
8. Plot the line whose equation is 4x - 3y + 9 G 0.
9. A line has slope m = -3 and y-intercept, -5. Write its equation.
10. A line has slope in = 5 and contains the point A(4, 1). Write its equation.
11. A line is determined by the two points A(-5,2) and B(-2, 0).Write its equation.
12. Graph the inequality x > 1 on the given system.
13. Graph the inequality y < 3 on the given system.
14. Graph the inequality. x . y <3 on the given system.
15. Graph y = 2 the given system.
16. Plot both of the lines whose equations are given below on the same setof axes and determine the common solution if one exists.
2x + y - 5 = 05x y - 2 = 0
B-132
208
17. Consider the system of equations y = -Zx +9 and 2x + 3y = 19.Find the common solution if one exists.
18. Find the common solution to the following system if one exists.2x - 5y = 63x - 4y = 9
19. EVALUATE:7I3
85
20. EVALUATE : 4-4 41 2 -3
21. Consider the system: 7x + 2y + 3 = 02x + 7y + 9= 0
The expression
1
:39 217
7 212 71
gives the (x or y) value of the common solution.
B-133
209
UNIT IX
NAME
Graph:: .1.nd Sentences in Two Variables PART IITest A B C D
TEACHER
SCORE
1. 6.
3.
4.
5.
all,-.Li--
4
T-I-
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r'I..-III
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.14.--,
B-134
210
7.
8.
SECTION
DATE
PERIOD
r-mr-r. 4
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9.
10.
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18.
19.
20.
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COMMONSOLUTION
UNIT X The Real Numbers PART ITest A
DIRECTIONS: Do not write on this test booklet. Place all answers on theanswer sheet provided to you. Do not spend too much time on any oneproblem.
1. Which of the following are not rational numbers? Write the letter(s) ofthe correct answer(s) on the answer. sheet.
A. 3
B.
C.
25
3
D. Ni 9
E. . 16
2. Arrange the following numbers in ascending order.3 45 7
1
93. Find a number between
8and by the average method.
4. Which of the following numbers are periodic?
A. 1.414 C. .666667
B. 1.8333333 D. .7515...MINISIBM
5. Express as a fraction in lowest terms .47 .
6. TRUE or FALSE: All rational numbers are also whole numbers.
7. COMPLETION: A rational number is the oftwo Weser..
8. COMPLETION: .45 written as a rational number in simplestform is
Write the letter of the correct answer on the answer sheet. If a and bare real numbers, then exactly one of the following is true: a >b,a <b, or a = b. This is a statement of the:A. Trichotomy Principle C. Reflexive Property
B. Density Property
15-136
2:1 2
D. Distributive Property
10. TRUE ow FALSE: Every rational number can be written asfinite decimal.
11. COMPLETION: 97 names a number which when squaredgives
712. COMPLETION: In Nrr , 7 is called the
13. Which of the following do NOT name a real number? Write the letter(s)of the correct answer(s) on the answer sheet.A. rm
B. NI 1
Simplify Problems 14-33.
14. ( k-5 )2
15. Nrrd- )2, where d > O.
16. ( Nr3 ) orf-
17. (5 ) (7 r18.
19. 11707-
120.
3 n27
21. 49x2y2
22. 4-2-6
23. 5 4-§-6--
24.
13-.137
213
C. NI 5
B-138
214
UNIT X The Real Numbers PART ITest B
DIRECTIONS: Co not write on this test booklet. Place all answers on theanswer sheet provided to you. Do not spend too much time on any one problem.
1. Which of the following are rational numbers? Write the letter(s) of thecorrect answer(s) on the answer sheet.
A. 3
B.
C.
25
.
7, I. .76
D. J9E.
2. Arrange the following numbers in ascending order. 3,
47 9
1 1
6Find a number between
7and by the average method.
4. Which of the following numbers are periodic? Write the letter(s) of thecorrect answer(s) on the answer sheet.A. .77773 C. 6.363
B. .626262... D. 1.6777
5. Express as a fraction in lowest terms .7 .
6. COMPLETION: A rational number is the of twointegers.
7. COMPLETION: .67 written as a rational number in simplest formis
8. TRUE or FALSE: All whole numbers are rational numbers.
9. Write the letter of the correct answer on the answer sheet. If a and bare real numbers, then exactly one of the following is true: a > b,a < b, or a = b. This is a statement of the:A. Density PropertyB. Reflexive Property
C. Distributive PropertyD. Trichotomy Principle
10. TRUE or FALSE: Every rational number can be written as a finitedecimal.
11. COMPLETION: J 57 names a number which when squaredgives
12. COMPLETION: In 4.3 , the index is
13. Which of the following do not name a real number? Write the letter(s)of the correct answer(s) on the answer sheet.
A. ./7-1-
B. NI 5
Simplify Problem., 14-33.
14. ('fr)2
15. ( )2, where d> 0
16. (r) ( Nr7-7-)
17. (3 Nril. ) (2 NI Z
NITT18.2
19. Ni 144a2
20. Nrir
al. J 64a2x2
22. Nri.ET
B-140
C.
23. 4 NI 48
24. /1275
25. 5
26.
2 ?. (Nrr3 ) ((\/ 85 )
28. (3 %r:fl2
29. Nr5b2
[5.130. 3
31. N/ (5xy)2
32. 3
3.3. V x
B -141
UNIT X The Real Numbers PART ITest C
DIRECTIONS: Do not write on this test booklet. Place all answers on theanswer sheet provided to you. Do not spend too much time on any one problem.
1. Which of the following are not rational numbers? Write the letter(s)of the correct answer(©) on the answer sheet.
32. Arrange the following numbers in ascending order. 2,
87
I I4
3. FUJ5
I a number between and by the average method.
4. Which of the following numbers are not periodic? Write the letter(a)of f correct answer(s) of the answer sheet.
C. 6.363
D. 1.6777
5. Express as a fraction in lowest terms .45 .
6. COMPLETION: .65 written as a rational number in simplest formis
7. COMPLETION: A rational number is the of twointegers.
8. TRUE or FALSE: All ratty nal numbers are also whole numbers.
9. Write the letter of the correct answer on the answer shoat. If a and bare real numbers, then exactly one of the following is tr,te: a >b,a 4b or a b. This is a statement of the:
A. Distributive Property C. Reflexive Property.
B. Trichotomy Principle D. Density Property
10. TRUE or FALSE: Every rational number can be written as afinite decimal.
11. COMPLETION: '4-71names a number which when squared gives
12. COMPLETION: In 47-3 the radicand is
13. Which of the following do not name a real number? Write the letter(s)of the correct answer(s) on the answer sheet.
A. ',FTC
B. 4-"F
Simplify Problems 14.33.
14. ( r-r)2
15. ( 4r7iC)2 where x> 0
16. ( 4-3-)
17. 14 ) z
18.
1 9 . 71 171,i
1
20. 4
21. NI 49y2x2
22. ,s112"
B.143
219
C, 471D. AU of the above are real
:umbers.
23. 3J24
24 J36
rr25. 3
2
26. "J3
27. (r) ( Nrirc)28. (4 47)2
29. 411a
30.
31. (L7a2)2
5a232. 3
33. krg
B-144
220
UNIT X The Real Numbers PART ITest D
DIRECTIONS: Do not write on this test booklet. Place all answers on theanswer sheet provided to you. Do not spend too much time on any oneproblem.
Which of the following are rational numbers? Write the letter(s) ofthe correct answer(s) on the answer sheet.
A. 4 F. NTT
3B. 7 G. krIT
5C. -9 H. NW
D. 44IT I. .62
E. .74
3 22. Arrange the following numberi in ascending order.5 3
3. Find a number between 1and by the average method.
4. Which of the following numbers are periodic? Write the letter(s) ofthe correct answer(s) on the answer sheet.
A. .773 C. 1.333
B. .727272... D. 7.272
5. Express as a fraction in lowest terms .
6. COMPLETION: .37 written as a rational number in simplest formis
7. COMPLETION: A rational number is the of twointegers.
TRUE or FALSE: All whole nvkmbera are also rational numbers.
B-145
221
9. Write the letter of the correct answer on the answer sheet. If a and bare real numbers, then exactly one of the following is true: a >b,a b or a = b. This is a statement of the:
A. Density Property C. Trichotomy Principle
B. Distributive Property D. Reflexive Property
10. TRUE or FALSE: Every rational number can be written as afinite decimal.
11. COMPLETION: In trry, 19 is the
12. 'COMPLETION: 451 names a number which when squared gives
13. Which of the following does not name a real number? Write the letter(s)of this correct answer(s) on the answer sheet.
A. tr:1 C. Nrr
B. 4-41T D. All of the above are realnumbers.
Simplify. Problems 14-33.
14. ( 4-5 )2
15. ( 3a )2, where a > 0
16. ( 2)17. (3 ArT) (7 4T)
4-14.
18.
19.
20. 412-
21. 81:2132
22. 411
B-146
222
B.- 1 47
223
UNIT X
NAME
The Real Numbers PART.ITest A B C D
TEACHER
SCORE
1. 18.
2. 19.
3. 20.
4. 21.
5. 22.
6. 23.
7 24.
8 25.
9. 26.
10. 27.
11. 28.
12. Z9.
13. 30.
14. 31.
15. 32.
16. 33.
17.
B-148
224
SECTION
DATE
PERIOD
UNIT X The Real Numbers PART IITest A
DIRECTIONS: Do not write on the test booklet. Place all answers on thepaper provided. Do not spend too much time on any one problem.
1. Write the letter(s) of the correct answer(s) on the answer sheet.Which of the following terms are similar?
Simplify Problems 2-8.
2. 41-2 + 3J2
3. NriT. + 3 - 8 Nrir
4. 5 4-T+ 6 13- 2 5
5. 5 + 3 8
6. 2 Nrfr - v7. ( 3 + Nr5) ( NI 3 - arc)
8. (1 - 4-3) (2 - 3
D. 7 42
E. 2 Nr-rr
9. W rite the conjugate of 3 - N 13
10. Write the conjugate of NI + 5
11. Simplify by rationalizing the denominator. 5
1 +
612. Simplify by rationalizing the denominator. +
B-149
225
Simplify Problems 13-19.
13. (-2 tea) (6 Nriai )
14. J1.5a2b
115.2
8a I 4123
j5a216. 3.
17. 2a
Solve and check for extraneous roots in Problems 20-22.
20. P.ric= 5
21. 45F+ 5 = 3
22. x + 7 = 4
e so'
UNIT X The Real Numbers PART IITest B
DIRECTIONS: Do not write on the test booklet. Place all answers on thepaper provided. Do not spend too much time on any one problem.
1. On the answer sheet, write the letter(s) of the correct answer(s).Which of the following terms are similar?
A. Nr.-5 D. 7 15
B. Nrr
C. 2 rrSimplify Problems 2-8.
2. 7 \IT - 3J3. Nfr - 6 NFT + 2Nr-3-
4. 4 T + 3'I7 + 10 NIT
5. 12 Nr-2-- 2 Nair
6. 3 455 + 718
7. ( Nr2 - NIT) ( + 7
8 . (2 - ) (3 - 3 NrT)
9. Write the conjugate of 9 + NMS- .
10. Write the conjugate of 4r-
11. Simplify by rationalizing the denominator.
E. 517
_ 1 ._ Simplify, by rationalizing the denominator.
:B-151
227
6
-
3
Simplify Problems 13-19.
13. (3 irc"-) (-5 )
14. N/21m2n
15. 18)7 -
7r216.16. 2
17. I ft
8a218. 4b
18g
19. 42iSolve and check for extraneous roots in Problems 20-22.
20. NTT = 7
21. Nr zri- 3 =4
22. 4-1+ 3 = 1
. B 152
228
UNIT X The Real Numbers PART IITest C
DIRECTIONS: Do not write on the test booklet. Place all answers on thepaper provided. Do not spend too much time on any one problem.
1. On the answer sheet, write the letter(s) of the correct answer(s).Which of the following terms are similar?
A. 4-5- D. 7 NrIT
B. r E. 11 \Fr
C. 3 4-g-
Simplify Problems 2-8.
2. 5 is/7- - 2 NF
3. Nrr - 12 Nrr + 9 NM-
4. 3 4-6- - 8 12 + 5 2
5. 6 /Tr + 2 417-
6. 10 20 + 3 NI 45
7. ( - NI 2 ) ( + rJ )
8. (3 + NfT) (4 + 2 5 )
9. Write the conjugate of Nri-11 4
10. Write the conjugate of J 2 + 3
11. Simplify by rationalizinj the denominator.
12. Simplify by rationalizing the denominator
B-153
229
2
4 - NrY
Simplify Problems 13-19.
13. (-447c) (3 qxy )
14. 6:n2n
15. 14-174r 42T
7x216.
j2
5
17
16nz218. 8n
27x__
19. NI 3x
Solve and check for extraneous roots in Problems 20-22.
20. Nrin= 3
21. NI r + 6 = 8
22. 47+ 9 = 2
B -154
230
UNIT X The Real Numbers PART IITest D
DIRECTIONS: Do not write on the test booklet. Place all answers on thepaper provided. Do not spend too much time on any one problem.
1. On the answer sheet, write the letter(s) of the correct answer(s).Which of the following tcrms are similar?
B. \r-fC. 3 2
Simplify Problems 2-8.
Z. 8 - 12 NI11
3. 4 4-1-+ 3 2 -
4. 3 NT-V-+ 3 NIT
5. 12 5 NI 20
6 . 10 N/715 + 3 125
7. (N/ 2 + 7 ) (qz - )
8. (2 ` 5 3) ('J- 2)9. Write the conjugate of + 5.
'10. Write the conjugate of \ri- - J 11
11. Simplify by rationalizing the denominator.
D. 2
E. 5
12. Simplify by rationalizing the denominator.
B-155
231
2
-
Simplify Problems 13-19.
13. (-4 N/ m ) (3 r\FT---ux )
14. NI I 4xy2
15. 1 r 18a
7c216. 3
517. 3x
25a
18. 5b2
50a
19. NrS--
Solve and check for extraneous roots in Problems 20-22.
20. 4a.= 10
21. = 2
22. pri--+ 5 = 1
B -156
UNIT X The Real Numbers
NAME
TEACHER
SCORE
1. 12.
2. 13.
3. 14.
4. 15.
5. 16.
6. 17.
7. 18.
8. 19.
9. 20.
10. '21.
11. 22.
B-157
233
SECTION
DATE
PERIOD
PART IITest A BCD
UNIT XI Relations, Functions and Variations Test A
DIRECTIONS: Do not write on this test booklet. Place all answers onthe answer sheet provided to you. Do not spend too much time on any oneproblem.
1. A (relation, function) is a set of ordered pairswhose first coorc-linates are all different.
Questions 2-5 refer to the relation whose table of values is given below.
x 1 2 3 4
Y 1 0 1 2
2. What is the domain of this relation?
3. What is the range of this relation?
4. On the answer sheet, write the letter(s) of the following orderedpairs which are coordinates of points on the graph of this relation.
A. (0,2)
B. (3, 1)
C.
D.
(3, 2)
(2, 4)
5.. Which one of the following is a formula for the relation? On youranswer sheet write the letter of the correct answer.
A. y = 12 - xl C. y = (x )2
B. y 2 - x D. y= x- 2
Questions 6-8 refer to the relation whose graph is shown below.
I i 1 5X
B-158
2 34
TRUE or FALSE: This relation is a function.
7. The domain of the relation is: (On your answer sheet write the le, tterof the correct answer.)
A. {1) C. {real numbers between 1 and 3 inclusive}
B. {1,4} D. {real numbers between 1 and 4 inclusive}
8. The range of the relation. is: (On your answer sheet write the letter'of the correct answer.
A. {1} C. {real numbers between 1 and 3 inclusive}
B. {1,3) D. (real numbers between 1 and 4 inclusive)
9. TRUE or FALSE: { (4, 9), (5,8), (4,-6), (3,8)) is a function?
Give the missing information for each of the functions below.
Domain
10. {1,3,5}
Range Formula
y = 2x - 3
11, {1 3, 5} .y = 2x - 1
12. If y varies directly as x in the roster below, state a formula givingy in terms of x:
x 2 4 8
'6 12 24..
13. Using the same roster as in number 12, what is the constant ofproportionality?
14. If y varies directly as x, and y = 6 when x = 5, what is y when x =6?
15. The elongation of a spring varies directly as the stretching force. If1C pounds stretches. a spring 8 inches, what force will Stretch it9 inches?
aQuestions 16-19 refer to the sentence bFor each expression in the
left-hand column, choose the appropriate answer in the right-hand column.
B-I59
235
16. and A. extremes
Ia-' 17.b
8. meansd
18. a and d C. proportion
19. b and r D. ratios
20. The length of the shadow of an object varies directly as his height.If a 6 foot mart casts a 4 foot shadow, how high is a building whichcasts a 120 foot shadow at the same hour?
21. Solve for X: X + 1 2X+ 72X - 7 X
Questions 22-24: For each statement in the left-hand column, write theletter of the correct formula in the right-hand column on your answer sheet.
22. y varies directly as x
23. y varies inversely as x2
24. xy varies directly as x2
A. y kx
13.
C.
kY
k=x
D. y =10,12
25. If y varies inversely as x and y = 6 when x = 7, what is y whenx = 3?
26. TRUE or FALSE: The drawing below is the graph of a directvariation?
13-160
26
1. If the table of values defines an inverse variation, then a =
2 1 i -a4 I. 3 a
3 161
UNIT XI Relations, Functions and Variation Test B
DIRECTIONS: Do not write on this test booklet. Place all answers onthe answer sheet provided to you. Do not spend too much time on any oneproblem.
1. A function is a set of ordered pairs whose (first, second)coordinates are all different.
Questions 2-5 refer to the relation whose table of values is given below.
x i 2 3 4
Y 1 0 1 4
Z. What is the domain of this relation?
3; What is the range of this relation?
4. Which of the following ordered pairs are coordinates of points on thegraph of this relation? Write the letter(s) of the correct answer(s)on your answer sheet.
A. (2, 4) C. (3,1)
B. (3,2) D. (0, 2)
5. Which of the following is a formula for the relation? Write the letterof the correct answer on your answer sheet.
A. y= 2 - x 2C. y = (2 - x)
B. y= 2 - x D. y= X - 2
Questions 6-8 refer to the relation whose graph is shown below.
3
0 L / 6
6. TRUE or FALSE: This relation is a function.
7. The domain of the relation is: (On your answer sheet write the letterof the correct answer. )
A. {1} C. {real numbers between 1 and 3 including I}
B. {1, 3} D. {real numbers between 1 and 4 including 4}
8. The range of the relation is: (On your answer sheet write the letter ofof the correct answer.)
A. {1} C. {real numbers between 1 and 3 inclusive}
B. {1,4} D. { real numbers between 1 and 4 inclusive}
9. TRUE or FALSE: { (4, 9) , (5,8), (3, 6), (4,1)) is a function.
Give the missing information for each of the functions below.
Domain
10. {1,3,5}
11.
Range
{1,3,5}
Formula
y = 2x - 3
y = 2x - 1
12. If y varies directly as x in the roster below, state a formula giving yin terms of x.
Ix 6 1 3 1 1
12141y 24
13. Using the same roster as in number 12, what is the constant ofproportionality?
14. If y varies directly as x, and y = 6 when x = 7, what is y when x = 6?
15. The elongation of a spring varies directly as the stretching force. If12 pounds stretches the spring 8 inches, what force will stretch it9 inches?
Questions 16-19 refer to the sentence a= . For each expression in the
left-hand column, write the letter of the correct answer from the right-handcolumn of your answer sheet.
B-163
239
a16.b
and
a17.b
and
18. a and d
19. b and c
A. means
B. proportion
C. ratios
D. extremes
2(.. The length of the shadow of an object varies directly an his height. If asix foot man casts a 5 foot shadow, how high is a building which casts a12t., foot shadow at the same hour.
21. Solve for a: a + 1 2a+2a -'7 a - 1
Questions 22-24: For each statement in the left hand column, write the letterof the correct formula in the right-hand column on your answer sheet.
22. y varies directly as x
23. xy varies directly as x2
24. y varies directly as 1
x
A. y = kx
B. Y =
C. Y= k2
D. y= kx2
25. If y varies inversely as x and y = 6 when = 1(., what is y when x = 3?
26. TRUE or FALSE: The drawing below is the graph of a directvariation.
B-164
240
27. If the table defines an inverse variation then a =
11111
x 3 2 -1
UNIT XI Relations, Functions and Variation Test C
DIRECTIONS: Do not write on this test booklet. Place all answers onthe answer sheet provided to you. Do not spend too much time on any oneproblem.
1. A (relation, function) is a set of ordered pairswhose first coordinates are all different.
Questions 2-5 refer to the relation whose table of values is given below.
x1
0 1 2 3
y 2 1 0I -
1
2. What is the domain of this relation?
3. What is the range of this relation?
4. Which of the, following ordered pairs are coordinates of points on thegraph of this relation? Write the letter(s) of the correct answer(s)on your answer sheet.
A. (0,2) C. (3,2)
B. (3,1) D. (2,4)
5. Which one of the following is a formula for the relation? Write theletter of the correct answer on your answer sheet.
A. y= (x - 2)
B. y = x - 2
2C. y= 2 - x
1). y= 2 - xl
Questions 6-8 refer to the relation whose graph is shown below.
B-166
242
6. TRUE or FALSE: This relation is a function.
7. Write the letter of the correct answer on your answer sheet.The domain of the relation is:
B. {1,4}
C. {real numbers between 1 and 4 inclusive}
D. {veal numbers between 1 and 3 inclusive}
8. Write the letter of the correct answer on your answer sheet.The range of the relation is:
A. {1} C. {real numbers between 1 and 3 inclusive}
B. {1, 3} D. {real numbers between 1 and 4 inclusive}
9. TRUE or FALSE: The set { (4,9) (5,8) (4, -6) (5,7)) is a function.
Give the missing inkrmation for each of the functions below.
Domain Range Formula
10. {1,3,5} y= 3x- 2
11. {2,5,8} y = 3x - 1
12. If y varies directly as x in the roster below, state a formula giving y interms of x:
I xy2 I 6
1
i 10 ..)1
13. Using the same roster as in Problem 12, what is the constant ofproportionality?
14. If y varies directly as x, and y = 5, when x = 4, what is y where x = 8 ?
15. The elongation of a spring varies directly as a stretching force. If.5 pounds stretches a spring 4 inches, what force will stretch it 7 inches?
Questions 16 -19 refer to the sentence a=
c. For each expression in the
left-hand column, write the letter of the correct answer in the right-handcolumn on the answer sheet.
B -16?
243
a c16. -1 -; andA. A. proportion
a c17. B.d= B. ratios
18. a and d C. means19. b and c D. extremes
20. The length of a shadow of an object varies directly as its height.If a 5 foot man casts a 3-1/2 foot shadow, how high is a buildingwhich casts a 120 foot shadow at the same hour?
21. Solve for y: 2y+ 7 y + 1y 1 2y- 7
In Problems 22-24, write the letter of the correct formula on youranswer sheet.
22. y varies directly as 1x A. y = kx2
23. y varies inversely as x2
24. xy varies dirt.ctly as x2
kB. y
2
C. kY
D. y = kx.
25. If y varies inversely as y = 6 where x = 7, what is y when x = 2?26. TRUE or FALSE: The drawing below is the graph of a direct
variation.
B-168
244
27. If the table of values defines an inverse variation, then A =A
x4
F
UNIT XI Relations, Functions and Variation Test D
DIRECTIONS: Do not write on this test booklet. Place all answers onthe paper provided. Do not spend too much time on any one problem.
1. A function is a set of ordered pairs whosesecond) coordinates are all different.
(first,
Questions 2-5 refer to the relation whose table of values is given below.
x -2 0 1 5
y 16 4 1 9
2. What is the domain of this relation?
3. What is the range of this relation?
4. Which of the following ordered pairs are coordinates of points onthe graph of this relation? Write the letter(s) of the correctanswer(s) on your answer sheet.
A. (5,9)
B. (4, 0)
C. (1,1)
D. (0,16)
5. Which one of the following is a formula for the relation? Writethe letter of the correct answer on your answer sheet.
A. y= 2 -x C. y = x - 2
B. y = (x - 2)2 D. y = 2 - x
Questions 6-8 refer to the relations.whose graph is shown below.
B-170
24S
6. TRUE or FALSE: This relation is
7. The domain of the relationship is: (Write the letter of the correctanswer on your answer sheet.)
A. {0,2,3}
B. {2, 1}
C. {real numbers between 2 and 3 inclusive}
D. {real numbers between 0 and 3 inclusive}
8. The range of the relation is: (Write the letter of the correct answer onyour answer sheet.)
A. {0,2,3}
B. {2,1}
C. {real numbers between 2 and 3 inclusive}
D. {real numbers between 0 and 3 inclusive}
9. TRUE or FALSE: { (1, 3), (-2, 5), (0, 4), (3, 5)} ika a function.
Give the missing information for each of the functions below.
Domain Range Formula
10. { -1, 0,1} y= 3x - 2
11. { -1, 3, 7} y= 2x+ 3
12. If y varies directly as x in the roster below, state a formula giving yin terras of x:
L-2
4.71
13. Using the same roster as in Problem 12, what is the constant ofproportionality?
14. If y varies directly as x, and y = 12 when x = 5, what is y when x = 2 ?
15. The compression of a spring varies directly as the force applied.If 5 pounds of pressure compresses the spring 2 inches, what forcewill compress it 5 inches?
Cuestions 16-19 refer to the sentencea
. For each expression in theleft-hand column, write the letter of the correct answer in the right-handcolumn on your answer, sheet.
B-171
247
16. a and d
17a and d
18. b and c
19. a=
cb d
A. ratios
B. proportion
C. means
D. extremes
iqh);20. The length of the shadow of an object varies directly as its heIf an 18 foot flag pole casts a shadow 12 feet long, what is the '1"gkEu'of a man whose shadow is 4 feet long at the same time?
21. Solve for k: 2k+ 7 k+ 1k 1 2k 7
Questions 22-24: For each statement in the left-hand column, writeletter of the correct formula in the right-hand column on your ansvsheet.
22. y varies inversely as x2 A. y= lac
23. xy varies directly as x2 B. y
124. y varies directly as xC.
kY =
2D. y= kx
25. If y varies inversely as x and y = 9 and x = 2, what is x wher,
26. TRUE or FAISE: The drawing below is the graph of a civariation. .
wowminum1111111111111
1111111110111
MO NM=11111111101111111111111111111111111111101111111111111111Na
111111111111111bW11111111111_
1111111111111111111101111M11
11111111111111111111111311111111
11111011111111
B-172
248
27. If the table of values' defines an inverse variation, then a =
ay
B-173
249
UNIT XI
NAME
Relations. Functions and Variatiell Test A B C D
TEACHER
SCORE
1. 15.
2. 16.
3. 17.
4. 18.
5. 19.
6. 20.
7. 21.
8. 22.
9. 23.
10. 24.
11. 25.
12. 26.
13.
14.
SECTION
DATE
PERIOD
APPENDIX C
ANSWER KEYS AND CHECK LISTS
FOR
A SELF-PACING PROGRAM IN ALGEBRA.
VOLUME I
C-'
21Acceptable Score
UNIT I TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
PART IITeat A
I. 1. A (5) VI. 1. 1 (7)2. A (5) 2. 15 (7)3. B (5) 3. 8 (7)4. B (5) 4. 12 (7)5. B (5) 5. 10 (7)6. C (5)7. B (5)
II. 1. True (3)2. False (3)
3. False (3)
4. True (3)5. False (3)
ILL 1. B' (6)
12. 3--2 (6)
3. 1 (6)
IV. 1. <B (4)
2. = A (4)
3. > C (4)
4. >C (4)
V. 1. B (6)
2. C (6)
3. D (6)
4. B (6)
Acceptable Score 2128
UNIT I TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
PART IITest B
I. 1. A (5) V. 1. B (6)
2. A (5) 2. D (6)
3. A (5) 3. D (6)
4. B (5) 4. A (6)
5. B (5)
6. C (5) VI. 1. 12 (7)
7. B (5) 2. 18 (7)
3. 16 (7)
II. 1. False (3) 4. 8 (7)
2. True (3) 5. 5 (7)
3. False (3)
4. True (3)
5. True (3)
III. 1. H (6)
2. 3 (6)
3. 2 (6)
IV. 1. > C (4)
2. >C (4)
3. = A (4)
4. >C (4)
C -4
253
29Acceptable Score -42
UNIT II TEACHERS ANSWER KEY
FIRST YEAR ALGEBRA
Test A
1. D (8) 22. No (10)
2. F (8) 23. No (10)
3. B (9) 24. x + 5 (10)
4. G (9) 25. a - 7 (10)
5. H (9) 26. 5 - n (10)
6. I (9) 27. 7c (10)
7. E (8) ...J. 2d + 6 (10)
8. 4 (8) 29. 3f - 2 (10)
9. 3 (9) 30. 5(m + 2) (10)
10. B (8) 31. 2w >3. (11)
11. E (8) 32. x + 7 = 15 (11)
12. 18 (8;9) 33. b3(9)
13. 36 (809) 34. 24 (9)
14. 7 (8.9) 35. (6a)2
(9)
15. 25 (8 9) 36. 0 (9)
16. 55 (8 9) 37. 1 (9)
17. Yes (10) 38. 16 (9)
18. Yes (10) 39. 32 (9)
19. No (1,0) 40. 8a2 (9)
...'70.20. Yes (10) 41. 27a3
(9)3
1
,....;2,"..
21. Yes (10) 42. 81x2 (9)
C-5
254
UNIT II
29Acceptable Score -41
TEACHER43 ANSWER XVI Test B
FIRST YEAR ALGEBRA
1.
2.
3.
A
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
D
F
B
G
H
I
E
4
3
B
E
16
64
5
25
30
Yes
No
No
Yea
Yes
(8)
(8)
(9)
(9)
(9)
(9)
(9)
(8)
(9)
(8)
(8)
(8, 9)
(8.9)
(8, 9)
(8, 9)
(8, 9)
(10)
(10).
(10)
(10)
(10)
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
4!1..
42.
No
No
x + 9
e. - 12
11 -11
Bc
Zd + 5
3f + 1
4(h + 3)
3w <2
y - 10
b3
24
(6a)2
0
1
16
32
82
27a3
81x2
26
(10)
( 1 0 )
(10)
(10)
(11))
(10)
(10)
(10)
(10)
(11)
(11)
(9)
(9)
(9)
(9)
(9)
(9)
(9)
(9)
(9)
Acceptable Score 29
UNIT 31 TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
Test C
1. D (8) 22. No (10)
2. F (8) 23. No (10)
3. B (9) 24. x + 2 (10)
G (9) 25. n - 5 (10)
5. H (9) 26. 2 - x (10)
6. I (9) 27. 17b (10)
7. E (8) 28. 3y + 4 (10)
8. 3 (8) 29. 2e - 1 (10)
9. 4 (9) 30. 3(a + 5) (10)
B (8) 31, 2n >5 (11)
E (8) 32. c+ 5= 15 (11)
12. 20 (8, 9) 33. (9)
13. 100 (8, 9) 34. 35 (9)
14. 8 (8, 9) 35. (5b)2 (9)
15. 49 (8,9) 0 (9)
16. 66 (8, 9) 37. k (9)
17. Yea (10) 38. 9 (9)
18. Yes (10) 39. 32 (9)
19. Yes (10) 40. 12b2
(9)
20. Yes (10) 41. 4b2(9)
21. No (10) 42. 125y3(9)
C-7
UNIT LI
9Acceptable Score z
TEACHER'S ANSWER KEY Test D
FIRST YEAR ALGEBRA
1. 1 (8)
2. G (8)
3. H (9)
4. E (9)
5. F (9)
6. D (9)
7. C (8)
8. 4 (8)
9. 3 (9)
10. A (8)
11. E (8)
12. 12 (8,9)
13. 36 (8,9)
14. 6 (8,9)
15. 64 (5,9)
16. 3:ii (5,9)
17. Yes (10)
18. No (10)
19. Yes (10)
20. No (10)
21. No (10)RS,C-8
22.
23.
24.
25.
26.
2 ?.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
No
Yea
y + 6
m - 8
12 - y
7d
7x + 4
3y - 1
7(h + 4)
4v >6
m + 21
b4
43
(7a)2
1
0
36
81
12a 2
8s.
9x2
= 43
(10)
(10)
(10)
(10)
(10)
(10)
(10)
(10)
(10)
(11)
(11)
(9)
(9)
(9)
(9)
(9)
(9)
(9)
(9)
W.
1.9)
30Acceptable Score40
UNIT III TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
Test A
1. 0 (15) 21. C (12)
2. 1 (15) 22. B (12)
3. b = R (12) 23. E (15)
4. 0 (15) 24. A (14)
5. 1 25. D (14)
6. 16 (15) 26. 5.3 (14)
7. 0 (15) 27. A (14)
8. 6 (15) 28. B (15)
9. 0 (15) 29. A (15)
10. No meaning. (15) 30. D (15)
11. No meaning. (15) 31. C (15)
12. by (15) 32. D (15)
13. 6RS33. 8
314. 32xy
1
15. False (13) 34.2
16. True (13) 35. 1
17. True (13) 36. B (15)
18. B (12) 37. 12A (15)
19. D (12) 38. 8q + 11 (15)
20. A (12) 39. 12v + 9w (15)
40. 6R+ 2S - 1 (15)
Acceptable Score 3076
UNIT III TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
Test 13
1. 1 (15) 21. B (12)
2. 0 (15) 22. A (12)
3. 0 (15) 23. A (10
4. 1 24. B (14)
5. B = D (12) 25. A (14)
6. 7 (15) 26. E (15)
7. 0 (15) 27. D (14)
8. 6 (15) 28. C (15)
9. No meaning. (15) 29. D (15)
10. 0 (15) 30. D (15)
11. No meaning. (15) 31. A (15)
12. 36a 32. B (15)
13. 5xy 33.3
1.. 63xy1
15. True (13)34.
9
16. False (13) 35. 2
17. False (13) 36. D (15)
18. C (12) 37. 156 (15)
19. B (12) 38. Ilq + 12 (15)
20. (12) 39. 16a + 7b (15)
40. 6a + 9b - 4 (15)
C-10
259
30Acceptable Score
UNIT III TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
Test C
1. 0 (15) 22. B (12)
2. 1 (15) 23. A (14)
3. a = Q (12) 24. D (15)
4. 0 (15) 25. E (15)
5. 1 26. A (14)
6. 20 (15) 27. C (14)
7. 0 (15) 28. D (15)
8. No meaning (15) 29. D (15)
9. 8 (15) 30. B (15)
10. No meaning. (15) 31. A (15)
11. 0 (15) 32. C (15)
12. 12w 33.5
13. 8RS1
14. 63xy 34. 6-
15. True (13) 35. 1
16. False (13) 36. D (15)
17. True (13) 37. 10a (15)
18. B (12) 38. 4w + 12 (15)
19. A (12) . 39. 23q + 3r (15)
20. C (12) 40. 7R + 3S - 1 (15)
21. D (12)
Acceptable Score 2076
UNIT III TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
Test D
1. N = B (12) 21. C (12)
2. 0 (15) 22. A (12)
3. 1 (15) 23. B (14)
4. 1 24. A (14)
5. 0 (15) 25. D (14)
6. 15 (15) 26. E (15)
7. 3 (15) 2?. C (14)
8. No meaning. (15) 28. B (15)
9. 0 (15) D (15)
10. No meaning. (15) 30. C (15)
11. 0 (15) 31. D (15)
12. 15a 32. A (15)
13. lxy 33. 1
14. 15xy 34.
15. True (13)
16. False (13)35. 3
7
17. True (13) 36. C (15)
18. D (12) 37. 17a (15)
19. A (12) 38. 10a - 5 (15)
20. B (12) 39. 16a 6b (15)41tH4%.
,4111.
40. 6x+ 3y+ 4 (15)
C -12-
Acceptable Score 3239
UNIT IV TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
PART ITest A
1. 5 (17) 20. 4 (20)
2. -3 (17) 21. 0 (20)
3. 0 (17) 22. True (20)
4. 78
(17) 23. 32 (18)
24. 4 (18)
51
4(17)
25. -7 (18)
6. False (1S) 26. -8 (18)
7. F (16) 27. -73 (18)
8. A (16) 28. 9 (18)
9. -1 (D) (16) 29. 36 (23)
10. Add (19) 30. 28 (23)
11. False (19) 31. -51 (73)
12. Reciprocal (25) 32. 4 (25)
13. Negative (16) 33. 2 (25)
14. -9 (19) 34. -4 (25)
15. 4 (19) 35. -5 (25)
16. 1- (19) 36. -18 (26)5
37. 8 (19)17. Zero (19)
38. -20 (19)18. Zero (19)
39. + 72 (19)1. 20 (20)
C-13
Acceptable Score 32
UNIT IV TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
PART ITest B
1. 4 (17) 20. 3 (20)
2. -6 (17) 21. 0 (20)
3. 0 (17) 22. True (20)
4. 56
(17) 23. 33 (18)
24. 4 (18)
5. 1
3(17)
25. -6 (.1.8)
6. False (17) 26. -1 (18)
7. B (16) 27. -80 (18)
8. E (16) 28. 13 (18)
9. C (16) 29. 24 (23)
10. False (19) 30. -30 (23)
11. False (19) 31. -68 (23)
12. Reciprocal (25) 32. 9 (25)
13. Positive (16) 33. 4 (25)
14. -7 (19) 34. (25)
15. 3 (19) 35. (25)
2 36. -6 h',26)16. -3 (19)
37. 17 (19)17. 0 (19)
38. -12 (19)18. True (19)
39. 32 (19)19. 16 (20)
C-14
283
Acceptable Score 3239
UNIT IV TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
PART ITest C
1. 3 (17) 20. 9 (20)
2. -2 (17) 21. 0 (20)
3. 0 (17) 22. True (20)
4. 38
(17) 23. 31 (18)
24. 7 (18)
5. 1
3(17)
25. -3 (18)
6. False (16) 26. -9 (18)
7. I (1) 27. -89 (18)
8. J (16) 28. 9 (18)
9. F (16) 29. 120 (23)
10. Add (19) 30. 21 (23)
11. False (19) 31. -34 r241
12. Reciprocal (25) 32. 5 (23)
13. Negative (16) 33. 2 (25)
14. -8 (19) 34. -5 (25)
15. 7 (19) 35. -5
16. 1 (19) 36. -9 (26)
37. 12 (19)17. 0 (19)
38. -19 (19)18. 0 (19)
39. 90 (19)19. 31 (20)
C-15
2P4
Acceptable Score 3239
UNIT IV TEACHER'S ANSWER KEY PART ITest D
FIRST YEAR ALGEBRA
1. 6 (17) 20. 4 C20)
2. -2 (17) 21. 0 (20)
3. 0 (17) 22. True (20)
4. 45
(17) 23. 23 (18)
24. 2 (18)
5. 1
5(17) 25. -7 (18)
6. False (16) 26. -2 (18)
7. G (16) 27. -58 (18)
8. D (16) 28. 11 (18)
9 I (16) 29. 36 (23)
10. False (19) 30. -24 (23)
11. Negative t19) 31. -45 (23)
12. Reciprocal (25) 32. 5 (23)
13. True (16) 33. 3 (25)
14. -6 (19) 34. -3 (25)
15. 2 (19) 35. -7 (25)
16. 5- (19) 36. -3 (26)
37. 3 (19)17. 0 (19)
38. -22 (19)18. True (19)
39. 27 (19)19. 17 (20)
C-16
fiUNIT IV
1. 1
Acceptable Score 1520
TEACHER'S ANSWER KEY PART IITest A
FIRST YEAR ALGEBRA
(25)
2. 1(25)4
3. if(25)12
4. 45
(25)
5. One (25)
6. Zero (25)
7. Positive (23)
8. Negative (23)
9. -15xy (23)
10. -8a 3 (23)
11. 4a 2 (23)
12. False (13)
13. True (13)
14. 5x (19)
15. -10y (26)
16. 8x + z (18)
17. x + y (19)
18. 12a - b (26)
19. -4y
20. +4
(19)
(8.9)
15Acceptable Score -id
UNIT IV TEACHER'S ANSWER KEY PART UTest B
FIRST YEAR ALGEBRA
1. 7 (25)
2. 1
8(25)
3. 3-4. (25)
4. 1 (25)
5. One (25)
6. Zero (25)
7. Odd (23)
8 . Even (23)
9. -245y (43)
10. 9a2y (23)
11. -2,7y3(23)
12. False (13)
1:. True (13)
14. 7x (19)
15. -12y (26)
16. 8x + z (18)
17. -2x. f 2y (19)
18. 6a + 2b (26)
19. 6x - 14y (19)
20. 1. (8,9)
C-18
Acceptable Score15R
UNIT IV TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
1.
2.
3,
1
3
1
5
13
(25)
(25)
(25)5
4. 5
6(25)
5. 1 (25)
6. 0 (25)
7. Positive (23)
8. Negative (23)
9. -15xy (23)
10. -bb3 (23)
11. 4c2 (23)
12. False (13)
13. True (13)
14. 7y (19)
15. -8x (26)
16. 9x z (18)
17. x y (19)
18. 13c - 2b (26)
19. y (19)
20. 1 (8.9)
PART IITest C
Acceptable Score1520
UNIT IV TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
1.52
(25)
2.1
6(25)
3.74
(25)
4. 1
5(25)
5. 0 (25)
6. 1 (25)
7. Positive (23)
8. Negative (23)
9. -6xy (23)
10. 16a2 (23)
11. -27a3 (23)
12. False (13)
13. True (13)
14. 7x (19)
15. 3y (26)
16. Ilx (18)
17. 6x + 2y (19)
18. 10a - h (26)
19. -4x - 3y (19)
20. 1 (8, 9)
PART IITest D
7/
UNIT V
24Acceptable Score -3-71.
TEACHEReS ANSWER KEY
FIRST YEAR ALGEBRA
1. A (27)
2. F (27)
3. H (27)
4. D (27)
5. True (27)
6. {3} (28)
7. (-12} (28)
8. { -7} (28)
9. { - (28)
11, {3}
12. 175
{-1(32)
14.
15. { 36}
17. {-12}
(28)
(29)
(29)
(29)
37 0}
19. { }
20.
22.
23. {
24. 11)
25. {24}
26. {5}
27.-1 01
28. b < -6
13
(29)29. d > 5
(29) 30. a < le
(29) 31. a <12
32. c >28
(29)
33, 4,
212 34. 90
C-21
Test A
(29)
(30)
(30)
(30)
(31)
(30)
(30)
(31)
(27)
(27)2 3 4 $ 6 7 8 9
(33)
(33)
(33)
(33)
(33)
(33)0 1 2 3
UNIT V
1. A
2. B
3. 1
4. G
5. True
6. {I}
7. {-11}
12. 1-15'}
15.
16. {-20}
17. {-16}
18.
Acceptable Score 24
TEACHER'S ANSWER KEY Teat 3
FIRST YEAR ALGEBRA
(27)19.
(27)ZO.
(27)21.
(27)
(27) 22.
(28) 23.
(28) 24.
(28)25.
(28) 26.
(28) 27.
(29)
28.(29)
29.
(29) 30.
(29)31,
32.
(29)33.
(29)
(29)34.
(29)
C-22
2 .?
{ ±}} (30)
{4} (30)
{-2} (30)
{ 12'} (31)
{2} 130)
{-1} 130)
4) (32.)
4 (27)
2.7)
0 1 2 3 4 5 6 7 8 9
b< - 2 (33)
d >13 :33)
a 5- 1-61 :33)
a <18 (33)
c < 15 (33)
-4 '3 -2 -1 0 1
$3
(33)
UNIT V
Acceptable Score2457
TEACHER'S ANSWER KEY Test C
FIRST YEAR ALGEBRA
1. A (27)
2. F (27)
3. FI (27)
4. D (27)
5. False (27)
6. {2} (28)
7. { -13} (28)
8. { -8} (28)
12.
13.
14. {-4}
15.
16.
(28)
(28)
(29)
(29)
19. {26} (30)
20.
21. { -3}
22. {}
23. {-
24. {- .1}
133}
26. 4)
(30)
(30)
(31)
(30)
(30)
(31)
(27)
27. -c-.--e..--1--f-40.10-0,......,..(27)
0 1 2 3 4 5 6 7 8 9
1228. < -5 (33)
(29) 29. b >6 (33)
(29)
(29)
(29)
1!30. x< 10
(3.3)
31. x < 18 (33)
R> :21- 2(33)
17. {-35} (29) 33. (33)5
18. (29) 34. 40
UNIT V
1. B
2. D
3. H
4. G
5. False
6. {2}
7. (-7)
8. {-14}
9. 3
10. {-11}
11. {4}
12.{ }
16. {4;4}
17. {-6}
18. {
24Acceptable Score 34
TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
(27) 20. {II}
(27) 21. (-3)
(27) 22. {1}
Test D
(30)
(30)
(31)
(27) 23. { ,I} (30)
(27) 24. {- 528.-} (30)
(28)25. {12} (31)
(28)26. 4 (27)
(28)27. (27)
(28) 0 1 2 3 4 5 6 7 8 9
(28) 28. y< - 2 (33)
(29) 29. d >12 (33)
(29) 30.1
- (33)
(29) 31. a <42 (33)
(29) 32. c < 16 (33)
(29)33. , (33)
-2(29)
34. 84(29)
(29)
(30)
C-24
Acceptable Score 25371
UNIT VI TEACHER'S ANSWER
FIRST YEAR ALGEBRA
Test A
1. E, F, G (34) 18. D (37)
2. C (34) 19. C (36)
3. 4 (34) 20. C (37)
4. 3 (34) 21. D (36)
5. B (34) 22. D (37)
6. A (34) 23. B (40)
7. D (34) 24. C (41)
8. B (34) 25. A (41)
9. D (35) 26. D (42)
10. A (35) 27. C (42)
11. B Z8. A (43)
12. C (36,37) 29. D (44)
13. B (36) 30. A (44)
14. B (37) 31. JD (44)
15. C (38) 32. 1 (39)
16. A (38) 33. a
17. C (37) 34. 36
C-25
2'74
25Acceptable Score 3 -4
UNIT VI TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
Teat 13
1. B,E,F, G, H (34) 18. B (37)
2. C (34) 19. D (36)
3. 5 (34) 20. A f37)
4. 5 (34) 21. B (36)
5. C (34) 22. A (37)
6. B (34) 23. C (40)
7. C (34) 24. B (41)
8. B (34) 25. C (41)
9. A (35) 26. D (42)
10. C (35) 27. B (42)
11. B 28. C (43)
12. D (36,37) 29. A (44)
13. A (36) 30. C (44)
14. C (37) 31: A (44)
15. A (38) 32. a
16. A (37) 33. 1 (39)
17. B (37) 34. 26
C-26
2 .? rt
Acceptable Score 2574
UNIT VI TEACHERtS ANSWER KEY
FIRST YEAR ALGEBRA
Tent C
1. E, G, H. (34) 18. D (37)
2. A (34) 19. D (36)
3. 4 (34) 20. B (37)
4. 3 (34) 21. A (36)
5. C (34) 22. B (37)
6. A (34) 23. D (40)
7. C (34) 24. D (41)
8. C (34) 25. D (41)
9. D (35) 26. C (42)
10. A (35) 27. C (4.2)
11. C 28. B (43)
12. C (36,37) 29. A (44)
13. C (36) 30. D (44)
14. C (37) 31. D (44)
15. B (38) 32. 1 (39)
16. B (38) 33. x
17. B (37) 34. 36
C- 27
276
Acceptable Score 2534
UNIT VI TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
Teat D
1. B,F,G (34) 18. C (37)
2. A (34) 19. D (36)
3. 5 (34) 20. A (37)
4. 4 (34) 21. B (36)
5. C (34) 22. D (37)
6. B (34) 23. B (40)
7. A (34) 24. C (41)
8. D (34) 25. D (41)
9. B (35) 26. B (42)
10. C (35) 27. A (42)
II. A 28. C (43)
12. B (36,37) 29. B (44)
13. C (36) 30. A (44)
14. A (37) 31. D (44)
15. C (38) 32. a
16. B (38) 33. 1 (39)
17. B (37) 34. 15,16,17 (39)
UNIT VII
Acceptable Score 2078.-
TEACHER'S ANSWER KEY Test A
FIRST YEAR ALGEBRA
1.
Z.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
A, C (45)
23 32 (45)
2xy3 (45)
6 (45)
2x2y (45)
12(3x + y - 2) (46)
5x(5x2 - 3x - 1) (46)
(x - 4) (x + 4) (48)
(a + 4)2 (51)
(b + 6) (b - 2) (52)
(3c - 2) (2c + 1) (53)
(x2 + 7) (x - 3) (46)
(5x - 9y) (5x + 9y)
2a (a + 5)2 (54)
(48)
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
2(2: + 2) (x - 2)
- 1 (x - 1)2
- 4:ed : 5x + 7
0
- 2:2 + 3x 1
{-1, 21
{0, 2}
{- 1 r 3}
{-5, 5}
{3}
{ -5, 2}
{any number}
{ }
4x + 3(20 + x) or
(54)
(54)
(57)
(55)
(57)
(55)
(55)
:55)
(56)
(56)
(56)
(55)
(55)
7x + 60
C-29
UNIT VII
Acceptable Score 20
TEACHER'S ANSWER KEY Teat B
FIRST YEAR ALGEBRA
1.
2.
3.
4.
5.
B
22 17
5xy4
6
3x3y4
(45)
(45)
(45)
(45)
(45)
15.
16.
17.
18.
19.
3(x + 3) (z - 3)
-I(x - 3) (x + 2)
0
-2x2 + 5x + 2
6x2 - 5x - 4
(54)
(54)
(55)
(57)
(57)
6. 9(x - 2y + 3) (46)20. { -4, 3} (55)
7. (x - 5) (x + 5) (48) 21. { -} , 4} (55)
8. 3x(x - 7) (x + 2) (46) 22. {0,3} (55)
9. (a + 6)2 (51) 23. {-4, 4} (56)
10. (b + 4) (b - 3) (52) 24. {5} (56)
11. 3(2d - 1.) (d + 1) (54) 25. {-3, -2} (56)
16. (x2 + 3) (x 7) (46) Z6. {any number} (55)
13. (3x - 8y) (3x + 8y) (48) 27. { } (55)
28. 12,13,1414. 3a(a 2 + 7a - 16) (46)
C-30
2)
Acceptable Score 2028
UNIT VII TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
Test C
1. B (45) 15. 4(c + 2) (c 2) (54)
2. 22 3 7 (45) 16. -1 (a - 1)2 (54)
3. 2a2b3 (45) 17. -6a2 + 3a + 1 (57)
4. 3 (45) 18. 0 (55)
5. 3a2b (45) 19. -y2 + 5y - 3 (57)
6. 6(3x + 2y - 4) (46) 20. {-1,3} (55)
7. 5x(4x2 - 3x + 1) (46) 21. { 0, 10) (55)
8. (x - 9) (x + 9) (48) 22. :"} (55)
9. Prime (51)23. (-9,9) (56)
10. (r + 10) (r - 3) (52)24. {4,6} (56)
11. (5y - 2) (3y + 1) (5.025. { -6,1} (56)
i2. (a2 + 5) (a - 3) (46) 26. {any munfrsr} (55)
13. 9(2r - 3s) (2r + 3s) (48) ?7. } (55)
14. x(x - 1)2 (54) 28. t = 3 hoe
C-31
28 :1
20Acceptable Score -a-
UNIT VII
1. A, B
2. 23. 7
TEACHER'S ANSWER KEY
rIRST YEAR ALGEBRA
(45) 15. 3(x + 3) (x - 3)
(45) 16. -1 (x + 1)2
Test D
(54)
(54)
3. 4xy4
(45) 17. 9x2 - 3x + 6 (57)
4. 8 (45)18. ,.2::z .. Gx + 7 (57)
5. 3x2y2 (45) 19. 0 (55)
6. 5(5x + y - 2z) (46) 20. {-6, 7} (55)
7. 12x(3x2 + 2x +1) (46) 21. { 0,3} (55)
8. (x - 6) (x + 6) (43) 22. {- 1 3} (55)
9. (y + 3)2 (51) 23. (-9,9) (56)
10. (b + 7) lb - 2) (52) 24. { -5} (56)
11. (3c + 2) (2c - 1) (53) 25. {.-4, 9} (56)
12. (x2 + 2) (x - 5) 46) 26. { } (55)
13. (7x + 9y) (7:c - 9y) (48) 27. {any uurnbar} (55)
28. 414. 4a(a + 5)2 (54)
C-32
Acceptable Score 18
UNIT VIII TEACHER'S ANSWER KEY
4. None
5. {2 -2}
6. Quotient
7. Numerator
8.
9
10.
11.
12.
67
4a5b
16x3y
1
x - 3
13. done
14.
15.
2xy
15x2
2
FIRST YEAR ALGEBRA
(58)
(58)
(58)
(58)
(58)
(58)
(58)
(59)
(59)
(59)
(59)
(59)
(59)
(61)
(61)
2
C-33
16.56x
17. (a - b) (m n)
18. 1
19. -10
9
20.
21.
22.
"I 26..0
24.
316y
5
6b5a
3
y) (x + 3)
3a+ 2
25. $22; $14
PART ITest A
(61)
(61)
(61)
(62)
(62)
(62)
(62)
(62)
(63)
Acceptable Score 18-27
UNIT VIII TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
1. {-1} (58) 16. -32. {2} (58)
1
x
17.3. {0} (58) (x + y) (a + b)
I. {5,-5} (58) 18. + 2c+ 4
5. None (58)2519. - -2-7-
6. Quotient (58)
7. Denominator (58) 20. 1
7y
88. (59)9 14xy221.
5
9.
10.
11.
3b4a
911z
2
1
5
x + 21". x- 313. Done
14. 2x
4x215.3
(59)
(59)
(59)
(59)
(59)
(61)
(61)
C..34
283
22. 1 2a
23.
24.
4x+ 2y
25. 9, 11
PART ITest B
(61)
(61)
(61)
(62)
(62)
(62)
(62)
(62)
(63)
Acceptable Score 13
UNIT VIII TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
1.
2.
3.
4.
5.
6.
7.
3.
10.
11.
12.
13.
14.
15.
16.
{2}
{_4}
{0}
{3,-3}
None
Numerator
True
9
(58)
(58)
(58)
(58)
(58)
(58)
(58)
(59)
(59)
(59)
(59)
(59)
(59)
(62)
(61)
(613
17.
18.
17n
20.
21.
22.
23.
24.
25.
5
gab4
3x2z2
Done
1
x+
4. 3- 3
6y
23a
54
C-35
284
1
-528
7x16yz
27x2y22
9ab2
10x + 16
500 seconds
PART ITest C
(61)
(61)
(62)
(62)
(62)
(62)
(62)
(63)
Acceptable Score 25
UNIT VIII TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
PART ITest D
1. {0} (58) 17. (x - y) (w - v) (61)
2. {3} (58)18. (a - 4)2 (61)
3. {-2} (58)5
19.6
(62)4. None (58)
5. {2,-2} (58) 20. 1 (62)7y
6. Quotient (58)21.. 32xyz (62)
7. Denominator (58) 5
8. (59) 375z522. (62)
98w3
9 3y2x
(59)
10.
11.
12a5c
1
x - 2
12. p + 4
(59)
(59)
(59)
13. Done (59)
15.
16.
x
15z2
2
40a7
(61)
C-36
2w,5
323. (62)(a - b) (a + 3)
24.+ 3)
3x
25. w = 7 1 = 15
(63)
Acceptable Score 1421
UNIT VIII TEACHER'S ANSWER KEYY.
FIRST YEAR ALGEBRA
1.
2.
3.
4.
6.
7.
8.
9.
10.
11.
7
9
- 3
(64)
(64)
(64)
(65)
(65)
(65)
(65)
(65)
(65)
(65)
(67)
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
5
4a - 2
4128
23a20
a + 2
x + 5
7b - 3a
a2b2
5x - 36
x2 - 81
2x2 4x - 7(x-4)(x+ 2)(x-1)
C-37
a+ ba - b
1:2
5{ 3}
{1}
PART IITeat A
(67)
(60)
(68)
(68)
1.63)
(68)
(68)
(69)
(69)
(69)
Acceptable Score 1421
UNIT VIII TEACHER'S ANSWER KEY
1.
2.
3.
4. 45
67
x - 58
3b - 3
38
5.3043a
FIRST YEAR ALGEBRA
(64)
(64)
(64)
(65)
(65)
6. x + 3 (65)
7. x + 6 (65)
5b + 2a
8. aab2
9
10.
4x - 21
x2 49
2x2 - 6x - 4
(x - 4) (x + 1) (x - 2)
11.
A B12. A + B
13. 1:2
r14. I. 3,
15. { }2
(65)
(65)
(65)
C-38
16. {-15}
17. {c >-2-93-}
{y> 1140
19. {-
20. 4
21. {1}
PART IITeat B
(68)
(68)
(68)
(69)
(69)
(69)
UNIT VIII
1.
2.
7
x - 58
4a - 2b
4. 4538
23a5. 20
Acceptable Score 14
TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
PART IITest C
(64) 16. {-15} (68)
17. {c >12} (68)
lfh.1410 1 (63)
1 1 I
(64)
1
(64)
(65)
19. (69)
20. ti? (69)
(65) 21. {-1} (69)
6. x 3 (65)
7. x + 5 (65)
8.
9.
10.
11.
12.
5b + 2a
a2br
5x - 36
x2 - 81
23c2 - 6x - 4(x - 4) (x + 1) (x - 2)
A - BA B
13. 1:2
a15. {3
(65)
(65)
(65)
(67)
(67)
(60)
(68)
(68)2J'
C-39
UNIT VIII
1.
2.
3.
4. 28
x - 35
3b - 3
41
5. 30
C
43a
6 . a + 2
7. x + 6
7b 3a8.a2b 2
14Acceptable Score
TEACHER'S ANSWER KEY
FIRST YEAR ALGELRA
cs1.
10.
11.
12.
13.
14.
4x 21
x2 - 49
2X1' . 4x - 7(x - 4) (x + 2) (x - 1)
y
m + n171
1:3
{ 3 }
PART YfTeat D
(64) 15. { I'} (68)
16. {-8} (68)
17. { c > 23}(68)
20(65) 18. {y > 7 } (68)
(65) 19. {-1} (69)
20. 4 (69)
21. {1} (69)
(64)
(64)
(65)
(65)
(65)
(65)
(65)
(67)
(67)
(60)
(68)
p
t
1 UNIT LX
Acceptable Score 22-F-8-
TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
. A (70,71)
(70,71)
3. 0 (70,71)
4. C (70,71)
5. G (70,71)
6. E (70,71)
7. B (70,71)
8. B (71)
9. E (71)
10. True (71)
11. True (71)
12. False (71)
13. 2
3 114 . y = 2- x -2- (72)
15. y= x+ 1 (72)2
16. y =7 x+ 4
17. z3
(72)
(72)
C-41
18.
PART 1Test A
19. (72)
20. 3
'al .3
t x -1 +1i 2y -1 0
(74)
(74)
22.
23.
(72)
(72)
24.
25.
26.
27.
28.
y =
A, D
-1
98
0 (72)
(72)
(73)
(73)
(73)
291C-42
Acceptable Scor.
22e
28
UNIT DC TEACHERS ANSWER KEY
FIRST YEAR ALGEBRA
1. B (70,71)
2. G (70,71)
3. C (70,71)
4. E (70,71)
5. J (70,71)
6. A (70,71)
7. I (70,71)
8. D (71)
9. E (71)
10. False (71)
11. True (71)
12. False (71)
13. 1
3 114. y=-4-x--4-
315. y= x2
816. y= -3x
17. 4
(72)
(72)
PART ITest B
18. (72)
19.
(72) 20.
(72)
C-43
2Te:3
22.
111111114:1111111111111M111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111111111
1111111111111111111111111101111111111111111111111111:711111111111111111111111111111111111.1111311(11111=111111
Illtr_TJITZ111111111111111111111111
(72)
1111111111U11111111111111n111111111111111111111111E.11111111111111111111111111NZ111111111111111111111
IIIIIIIIit1111111111111111E4
111111111111111131111
11111,11111111101112 MIS111 11111111111
x -3 -1 3
y 3 -1 -9
22. (72)
23. (72)
KIM irAllimura MINS11111111111111111111.11111111111111111111111111111111111
laIRMINIMEIEP1111111111111111111111111111
1111111111110111101111.111111111111111111111111111111
1111111111111111111111111111111
X MM
24.
25.
26.
27.
28.
x=
A,D
23
5ave
2
0 (72)
(72)
(73)
(73)
(73)
C-44
293
g2Acceptable Score28
UNIT IX TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
1. C (70,71)
2. E (70,71)
3. D (70,71)
4. A (70,71)
5. F (70,71)
6. I (70,71)
7. B (70,71)
8. D (71)
9. E (71)
10. True (71)
11. True (71)
12. False (71)
13. 3
14. y = -3- x + 1 (72)
15.1y= x+ 3 (72)
16;10
3(32-).
17. 9 (72)
C-45
2,34
PART ITest C
18. (72)
19. (72)
uminleFiii
RIEll
11111111111111/11111111
11111111174111111111
ME 1111111t11111111111111111FANIIIII0
L1W11114111i61111111111011
11111111117M1111111111111111111E1111111111111011111111111111111111
. 3
-3 -1 3
21. 53
(74)
/74)
p 22. (72)
23. (72)
24.
25.
27.
28.
x =
A, C
65
10
0 (72)
(72)
(73)
(73)
(73)
9
C
UNIT DC
1. B
2. A
3. J
4. D
5. E
6. H
7. G
8. E
9. C
10. False
11. True
12. False
13. 4
6 114. y=gx--g.
3 515. yr4 -i-x+i
9 916. y= --4-x+
17. 13
Acceptable Score 2228
TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
(70,71)
(70,71)
(70,71)
(70,71)
(70,71)
(70,71)
(7 0, 71)
(71)
(71)
(71)
(71)
(71)
(72)
(72)
18.
PART ITest D
(72)
19.
(72) 20.
(72) 21.
C-47
2'4E1
(72)
x -3 -1Y : 3 2 0
(74)
(74)
22.
23.
(72)
(72)
24. True (72)
25. A C (72)
26. 2(73)
27. 5 (73)
28. C (73)
C- 48
2'317
UNIT IX
15Acceptable Score21
TEACHER'S ANSWER KEY
imIRST YEAR ALGEBRA
1. Negative (73)
2.
MAIMOMMINEU EEMMUMNIMMEMMEM
MEMOSESSMIVEmummonoNEwMVI
(72)
3.
4.
5.
m =
rn =
3
32
(74)
(74)
(74)
am ammummammeMEMUDnnmemmummumampliammadisEEMMEMPMMENEOMMORIAMAEOM1111192111111EMA
7.
PART IITest A
MEMMEMMMINIMMM1111110
NAM RMEMOME
(74)
AMONminnamminMA
MIONEWIMMEMMIImmominsmummiammiumm
nor mamma
8. (74)
mummisammmmattram eo nQNOWwitotmomommm011-dA d
orammummumms1.MEV2 EOM9. y = -2x + 1 (75)
10. y = 3x - 5 (75)
(74)11. y= -x (75)
298
12. (76)
13. (76)
14.
MN NSENNMEMIERWZOKUOSNAMOOMMOOMOOMIIMMOOWNOWNOMOlommannomumwrONSWIIMONNEMOMEMMWEOMMUOUINMEIGIMMUOMMENA UM UN
15.
16.
(76)
AIUM AIMW =RAMMWENEM01111110MWENANN
IONMEMMOMMOOMMOMMMIIMMEOMNMUE2111111111
(77)
{(2,1)}
17. {( -2,5)} (78,79,80)
18. {(-3,-2)} (78,79,80)
19. 22 (81)
20. -7 (81)
21. y (81)
Acceptable Score
UNIT IX TEACHER'S ANSWER KEY
1. Positive
2.
FIRST YEAR ALGEBRA
1521
PART IITest B
(73) 7. (74)
(72)
UMNIIMMMOGSMOMMMEN
MWMOOCENNUMMMUMMEMMEMMatingilEMMEMOMMEiMMOMMOM
MMUMOMMOMMUMMOIMM
3. m= 5 (74)
4.4m= -3 (74)
5. (74)
6.
MM.1111111111111
111111111111111Millial
INIMIIIIIIK1151111111111111111111111112M1111111811111,41111$11111NINIRE111111111111111111111111111111ralt
21111WOMMON BRAMMMEMIPM MIMI=mmaammumUMWMAMmarrU111111111MOIMMWMMINIMIME 41111111
(74)
(t4) 9.
10..
11.
y= -2x4 2
y = 3x 8
y= -x - 1
(75)
(75)
(75)
C-51
12.
13.
(76)
(76)
aMM III
% !
NOIR MRananams.kMWINN
Mk IIIIMM'IN
WINARO 1IPAail VI
14. (76)
C-52
3 1
15. (76)
LEI 11MUM NMUMW. MA111111,!raMil12111111110011111
IIMMUMI
16. (77)
{ (2,1 )}
17. { (2,3)} (78, 79, 80)
18. { (- 3, -2)} (78, 79, 80)
19. 48 (81)
20. -9 (81)
21. (81)
UNIT IX
1. Negative
2.
15Acceptable Score ri
TEACHERTS ANSWER KEY
FIRST YEAR ALGEBRA
(73)
(72)
7.
PART IITest C
(74)
3.
4.
5.
m =
m =
-2
5-
3
(74)
(74)
(74)
8.
6.
I ,
EmsIIIIPik
Nri 1
LL..-- -
(74)
11 n
9. Y= - 3 (75)
10. y = -2x + 5 (75)
11. y = 2x - 2 (75)
12.. (76)
13.
14.
(76)
(76)
IMOWM=IIIWAVIIME
,.. 1111/MISkiaMPatietili3110.
bRI=2111 501IF 41If WO
15. (74)
16. (77)
INIMMIN11111111111MUM
17412111111111111Pie MOM
PS * IMPMO, a
{ (.-2,5)}
17. {(17,11)} (78, 79, 80)
18. { (3, -2)} (78,79,80)
19. 12 (81)
20. -14 (81)
21. x (81)
C-54
3 11 3
Acceptable Score 1521
UNIT IX TEACHER'S ANSWER KEY
1. Positive
2.
FIRST YEAR ALGEBRA
(73)
(72)
PART IITest D
7. (74)
3.
4.
5.
m =
m =
7
3-
5
(74)
(74)
(74)
8.
am amUIV".
111111Ell_
vivo1011011MR.1110111111!MI
vi
III
6. (74)
EI VEN1111M1011 nos
11111111:1111111111111111110111M=
1111.1111NMEINUMMNIMIONINIONN
11111111111111111111 EllC-55
304
9.
10.
11.
(74)
y = -3x - 5
y = 5x - 19.
3y = -2x - 4 (75)
(75)
(75)
12.
13.
14.
(76)
(76)
(76)
RPM11111111MMONNWIMMMONORMMWMMUNINMMAIMMEMOIMMOU1111111101111MOOMMMEOWSMONUMNMIUMNOWOOMMEIMMENNOUMMMEMEMMIIN
C-56
305
15.
16.
(76)
is
{(/ , 3)}
17. { (2,5)} (78,79,80)
18. { (3, 0)} (78,79,80)
19. 11 (81)
20. 4 (S1)
21. (81)
23Acceptable Score
UNIT X TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
I.
2.
3'
4.
5.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
11.
18.
G, H, I
4 3
17144
B,D
47
(85)
(82)
(82)
(83)
(83)
(83)
(82)
(83)
(33)
(83)
(84)
(84)
(84)
(84)
(86)
(86)
(86)
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
99
False
Ratio
920
A
False
97
Index
B
5
7d
krrl
35 4-6-r
krT
PART ITest A
10z (84)
Prs- (86)
7xy (84)
2 kir (86)
20 Nar (86)
5 (86)3
NITC (86)7
34.2_ (86)
2A ri- (86)
25B (86)
a WT. (86)
(86)7
lab (84)
x (86)
(86)
UNIT X
1. A,B,C,D,E,I
2. 3 47 ' 9
3. 1384
4. B,D
95.
6. Ratio
677. 100
8. True
9 D
10. False
11. 57
12. 7
13. A
14. 7
15. 6c1
16. 35
17. 6 NI 62-
18. J 5
Acceptable Score 23
TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
(85) 19.
(82) 20.
21.
(82) 22.
(83) 23.
(83) 24.
(E.2) 25.
(83)26.
(83)27.
(33)28.
(83)29.
(84)
30.(84)
31.
(84) 32.
(84)
(86)33.
(86)
(86)
12a
NT-3-
8ax
3 4 2
16 Nii.
47--
PART ITest B
(84)
(86)
(84)
(86)
(86)
(86)
(86)
(86)
(86)
(86)
(86)
(86)
(84)
(86)
(86)
4 155
3 NI 55
28 4-1-
9y
b 4r5a3
5xy
a 421-3
NN_u
UNIT X
Acceptable Score 2333
TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
1.
2.
3
4.
5
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
F, G, H
2 37
(85)
(82)
(83)
(83)
(83)
(83)
(82)
(83)
(33)
(84)
(84)
(84)
(84)
(84)
(86)
(86)
(86)
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
40
A, C
511
1320
Ratio
False
B
False
73
15
8 Nri6
Nrg-
PART ITest C
9a (84)
NrT (86)
7yz (84)
2 4T (86)
6 4-6- (86)
73' (86)6
p,r6 (86)
2 ,,rs3
(86)
2c 4 3 (86)
16y (86)
a 11 (86)
2(86)
Tab (84)
a Nrrg (86)3
ab (86)
Acceptable Score 2333
UNIT X TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
I.
2.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18-
A,B,C,D,E,I
2 3
3 5
13
(85)
(82)
(82)
(83)
(83)
(83)
(82)
(83)
(33)
(83)
(84)
(84)
(84)
(84)
(86)
(86)
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
84
B, C
5
9
73
100
Ratio
True
C
False
Radicand
52
A
5
3a
1.--Tf
21 21
C-60'
3099
PART ITest D
8a (84)
NTT (86)
9ab (84)
3 NI 5 (86)
12 4170- (86)
4-2T (86)
NI3 7 (86)
9
3B Nrc-- (86)
9a (86)
a 4 lY (86)
(86)11
(86)
flab
a
(84)
(86)
(86)
UNIT X
1. B,D
2. 7 4-1-
3. -4 4I1-
4. 11 NiT - 2 4-8-
5. 11 4-2
6.
7. -2
8. 11- 5)3
9. 3 + 411
10. 47 - NTT
11. -5(1 -
12. -3( 41 - r13. -12a 4-17
14. a NI 15b
15. 2a NrE7
16.
Nnii17. 2a
18. Y-3 -3cx
Acceptable Score 16
TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
(87) 19. 2 Nri--cz
PART IITest A
(86)z
(87) 20. {25} (90)
(87) 21. {4} (90)
(87) 22. 4 (90)
(87)
(87)
(88)
(88)
(89)
(89)
(89)
) (89)
(86)
(86)
(86)
(86)
(86)
(86)
C-61
Acceptable Score 16
UNIT X TEACHER'S ANSWER KEY
FIRST YEAP. ALGEBRA
1. A, D (87)
2. 44 5 (87)
3. -3 (87)
4. 7 4-7+ 10 (87)
5. 6.4-2 (87)
6. 29 Nrr (87)
7. -5 (88)
8. 12 - 9 42- (88)
9 9 - 4 10 (89)
10. 43 + (89)
11. 3( 3 + 1) (89)
3( NI 2 + )12. (89)-5
13. -15c 47ci (86)
14. m 42173. (86)
15. 2x (86)
R16.
Nrit (86)2
Nrgi17. 2t
18.b
2b (86)
(86)
PART IITest B
19. 3 .JR'h (86)
20. {49} (90)
21. {19} (90)
22. 4 (90)
.111111411W.
Acceptable Score16
UNIT X TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
1. A, C (87)
Z. 3 6 (87)
3. -2 NIT (87)
4. 3 4-6-- - 3 tra- (87)
5. 12 NTT (87)
6. 29 4-3- (87)
7. 4 (88)
8. 22 + io J 5 (88)
9. Nni +4 (89)
10. 3 (89)
11.4 + (89)
12. -( 4-2+ 4-37)
13. -12x
14. m41371
15. ZR 4-3-
rri16.
x s
15m17.
18.
3m
2n
(89)
(86)
(86)
(86)
(86)
(86)
(86)
C-63
312.
PART IITeat C
LIE_ (86)x
20.
21.
22.
{9} (90)
{58} (90)
40 (90,
UNIT X
1. D, E
2. -4 11
3. 6 NI 2
4. -4 + 3 4
5. -2 4T
6. 45 NIT-
7. -5
8. 16 - 7 Nfr
9. -510. 4-1 +
11. _2( + 2)
+12.
9
13. -12m NriT
14. y Nrrtrii
15. a J 6
Nfif16.
3
NriSr17.
18.
3x
b
Acceptable Score1622
TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
PART IITest D
(87) 19. =b (86(86)
(87) 20. (100) (90)
(87) 21. {7} (90)
3 (87) 22. 4 (90)
(87)
(87)
(88)
(88)
(89)
(89)
(89)
(89)
(86)
(86)
(86)
(86)
(86)
(86)
C4.4
313
Acceptable Score 1927
UNIT XI TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
Test A
1. Function (92) 19. 13 (93)
2. {1,2,3,4} (91) 20. 180 (93)
3. {0,1,2} (91) 21. {-4, 4} (93)
4. B (91) 22. B (94)
5. A (91) 23. C (93)
6. False (92) 24. A (93)
7. D (92) 25. 14 (94)
8. C (92) 26. False (93)
9. False (92) 27. -1 (94)
10. {-1,3,7} (92)
11. {1,2,3} (92)
12. y = 3Y, (93)
13. 3 (93)
14.36
5 (93)
15.
16.
5,44
D
(93)
(93)
17. C (93 )
18. A (93 )
C-65
3 4
19Acceptable Score
UNIT XI TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
Test B
1. First (92) 19. A (93)
2. {1,2,3,4 (91) 20. 144 (93)
3. {0,1,4} (91) 21. a= +4 (93)
4. C (91) 22. D (94)
5. C (91) 23. A (93)
6. False (92) 24. B (93)
7. C (92) 25. 20 (94)
8. D (92) 26. True (93)
9. False (92) 27. -9 (94)
10. {-1,3,7} (92)
H. {1,2,3} (92)
12. y = 4x (93)
13. 4 (93)
14. 36.(93)7
15. 272
(93)
16. (93)
17. B (93)
18. D (93)
C -66
3 5
UNIT XI
1. Function
2. {0,1,2,3}
3. {0,1,2}
4. A, B
5. D
6. True
7. C
8. D
9. False
10. {1,7,13}
11. {1, 2,3}
12. y= 1
x
13. 2
14. 10
15. 354
16. B
17. A
18. D
Acceptable Score 19
TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
Test C
(92) 19. C (93)
(91) 20. 1200(93)
(91)21. + 4 (93)
(91)22. C (94)
(91)23. B (93)
(92)24. 13 (93)
(92)25. 21 (94)
(92)26. False (93)
(92)27. -1 (94)
(92)
(92)
(93)
(93)
(93)
(93)
(93)
(93)
(93)
Acceptable Score 1.-97
UNIT XI TEACHER'S ANSWER KEY
FIRST YEAR ALGEBRA
Test D
1. First (92) 19. B (93)
2. {-2, 0,1, 5} (91) 20. 6 (93)
3. {16,4,1,9} (91) 21. {i- 4} (93)
4. A, C (91) 22. B (94)
5. B (91) 23. A (93)
6. True (92) 24. C (93)
7. D (92) 25. 6 (94)
8. B (92) 26. True (93)
9. True (92) 27. 3 (94)
10. {-5, -2,1} (92)
11. {-2, 0, ill (92)
12. y = -2x (93)
13. -2 (93)
14. 24(93)5
15.2 5
(93)2
16. D i (93)
17. A (93)
18. C (93)
C-68
3 1;
APPENDIX D
PROFILE SEEET
FOR
A SELF-PACING PROGRAM IN ALGEBRA
VOLUME I
D -1
Name of Student:
Subject:
SCAT ScorP,s:
STUDENT PROFILE SHEET1elm lir es offmmiliaCasraWsImeasmi
Quarter Grades:
H. R.
Pd.
1001.00. yimal=1.01141...m.M
I II PI III IV H Y
I .1
Test No. Date AcceptableScore
Studenti Score
Comments Dates ofAbsence 1__
A
i I-I' I
Ii
4
.. ....--...---......-....
I-..--..-.--4-..---..-..-...--...........-........-........--.....-.-.-.....-..-...
....-.........
-1
I
.:
i
....--..----.-.--1--1
4 - -I
.,
i
a- z
Name of Student:
I C . , l . 4 ., V ' J. /el , . . ;..: A. ... (,0t: ; .. I . ...)
%... 0 re
. t ..,{.4..414..
3core: \ ... r.)... r 1 1 !I e il L
Absence
__......_ .... .
_..........._................
......_. ___, .......
.... _....................._
. .
...._ 4-
...............____ ....._
1._
-+--
Anecdotal Record:
320
APPENDIX E
EVALUATION SHEET
FOR
A SELF-PACING PROGRAM IN ALGEBRA
VOLUME I
321E -1
REACTIONS PLEASE
This program wil/ only be as good as you make it. Yoursuggestions and criticisms are earnestly sought so that they can beincluded in revisions of the program.
VOLUME I
Page Number (if appropriate) Comment
Send to: Thomas E. RowanSupervisor of MathematicsMaryland State Department of Education600 Wyndhurst AvenueBaltimore, Maryland 21210
E-2
322
